You tread a pre-biased road as you seek a set of axes' names to describe "personal preference" with the traditional Fudge adjective ladder.  While the endpoints might be polar opposites (e.g. between Superb Verbalness to Superb Mathiness), you will make few friends referring to Superb Mathiness as Terrible Verbalness.  Alike the typical Fudge scalars where players/GMs acknowledge the loss of potency as the adjectives drop lower and lower, most (if not all) the spectra you seek to describe grow stronger as the advocates move more towards their preferred end (in their value system, at least).  What you need is a U-shaped series of adjectives that never use a diminishing adjective, but switches between the antonyms as it moves away from the balanced middle.

For example:

You are, of course, correct and you caught me. I was slanting the idea of play style descriptive traits to the Fudge scale purposefully to generate reactions and responses.  Which I guess was successful in that you saw the bias and responded!

You also need to make sure that every axis actually measures two traits that directly oppose. For instance, verbalness and mathiness really don't oppose, one can put extremely complicated mechanics in place that only use the adjectives. However, opinion of the adjective scale on a number-adjective basis is directly opposed, though it may well vary highly within a single GM.

Knaight wrote:

You also need to make sure that every axis actually measures two traits that directly oppose. For instance, verbalness and mathiness really don't oppose, one can put extremely complicated mechanics in place that only use the adjectives. However, opinion of the adjective scale on a number-adjective basis is directly opposed, though it may well vary highly within a single GM.

Also true and very fair criticism. Still my basic question remains: What attributes define RPGs? Almost all Boardgames now come with at least three attributes:
"Number of players", "Playing time", and typically "Age" or "Complexity" (Age being a presumed measure of how simple or complex the game is). You can see these on the outsides of most Boardgames published in the last decade - especially European boardgames. So what are the defining traits for a set of RPG rules  - not a world setting, but the rules themselves - system like Fudge, GURPS, D20, Hero's D6 system and so on.

I still maintain that one trait has to be some indicator or simplicity to complexity. Another is, using what ever adjectives you might like, rigidity to flexibility (or structured to unstructured). Another might be universality - can the rule be applied to widely different settings. A quick Google search didn't turn up much. See http://kuoi.com/~kamikaze/RPG/classification.php for an attempt at classification (which is not the same a defining a set of traits). As RPG system often reflect play styles and vice versa, looking at attributes for RPGs might suggest attributes for play style.

Whether or not different play styles can be said to be opposites along a linear scale, I think there are some clear preference among player out there. Some people love detailed rules and other abhor them. Some people like to focus on accomplishments (kill the monsters, take the loot - to over state the extreme) and other could spend 50 hours doing in-character dialog among themselves (also to over state the extreme). I am sure there are other clear preferences that are (or seem to be) opposites that I haven't listed.

One could always use GNS theory, its actually workable if you ignore the details and massive bias towards N in the original model. Then there is the matter of modeling GM styles as opposed to game styles. Looking at both:

Game Styles:
Reliance upon GM judgment

Overall Resolution (Similar to the term used for optics, as opposed to graininess, which somehow managed to get two completely opposite definitions)

System Mechanical Weight (A measure of rules quantity, basically how mechanically heavy the game is)
Setting Reliance (A measure of how poorly the game can model other settings)

Character Mechanical Weight (A measure of mechanics attached to a character, similar to system weight).
GM Styles:
Authority (The extent to which the GM is dominant over the game)

Improvisational Preference

Neutrality (The extent to which the GM neither sides with or against the players)

Focus (The extent to which the GM focuses upon the game and not table chatter)

Obviously there are more, but those should be workable. Using myself and Titled (my game, its in the Other Games forum somewhere) as examples, its easy to set stats.
Titled
Judgment Reliance: Great (The GM needs to set difficulties on a word scale, and decide Title applicability, both of which are judgment calls)
Resolution: Poor (There are 5 attribute and difficulty levels, and 4 Title Applicability levels. Then there are no hard modifiers at all)
System Mechanical Weight: Terrible (Its 4 pages, with examples consisting at least 2 of them. The rest is due to unnecessary verbosity that makes A New Dimension to Gunfire look concise by comparison)
Character Mechanical Weight: Terrible (Its three attributes, one to three titles, and one nature. If you can't fit this on a 2cm * 4 cm scrap of paper, you need to check your fine motor skills)

Knaight as GM
Authority: Poor (I'm yet another player. Nothing more, nothing less.)
Improv: Superb (Planning: I hate it, I rarely do it, and I have a bad habit of building settings on the spot, and always create scenarios on the spot based upon what characters are created.)
Neutrality: Good (I just operate the setting, but if players lack creativity I'm not above dumbing down the opposition)
Focus: Terrible (The game is one tiny part of what is going on, not the focus by any means)

Knaight wrote:

Game Styles:
Reliance upon GM judgment
Overall Resolution (Similar to the term used for optics, as opposed to graininess, which somehow managed to get two completely opposite definitions)
System Mechanical Weight (A measure of rules quantity, basically how mechanically heavy the game is)
Setting Reliance (A measure of how poorly the game can model other settings)
Character Mechanical Weight (A measure of mechanics attached to a character, similar to system weight).
GM Styles:
Authority (The extent to which the GM is dominant over the game)
Improvisational Preference
Neutrality (The extent to which the GM neither sides with or against the players)
Focus (The extent to which the GM focuses upon the game and not table chatter)

Knaight - a really good set of possible attributes. Thanks. Resolution in the only one that just doesn't click for me (not sure why). I think I'd prefer 'detail' or 'depth' perhaps. Have to think about that for a bit.

I am still hopping that in time some other folks may chime in with their own ideas of attribute sets to describe any or all of (a) RPG system, (b) GM style, (c) play style, which could be all one, combined in to two, or three different sets of attributes. I still think player and GM styles tend to synch (otherwise players find other GMs and vice versa) and then players and GM tend to gravitate towards an RPG style that fits their style or play, so I am still thinking a single attribute set might be able to describe all three.

I guess it shows my newbiness when I read this discussion and it took me a little while to figure out what the point of this discussion was. As a new GM I seem to follow a pattern of my teacher. In this case Wolf "SirWolf" on the Fudge IRC forum is one of the ones who have continued to point me to different ways of doing things and so here are what I  believe are my stats:

Blood In Space

Rule: Fair (I tried to design Blood In Space pretty close to the original Fudge source material so the rules aren't to heavy.)

Resolution: Mediocre  (with all the weapons and the armor, resolution gets a little slow when doing on the math for finding out damage in Simultanious combat rounds.)

System Mechanical Weight: mediocre (The system is still some-what convoluted, but it's still in work)

Character Mechanical Weight: Fair (The character is based off of the way that fudge puts them together).

JonathanS as GM
Authority: Fair (Military background makes me want to take command if I'm in charge. My problem is not to get bossy. )

Improv: Mediocre (I plan out my worlds generally. I'm familiar with everything in it, but don't lock the story down so the character's have free movement. This does throw loops at me sometimes though.)

Neutrality: Good (it's for the story and for the players. Whatever makes it fun for the people!)

Focus: Mediocre (I get easy sidetracked and confused with the system, but the story and the players have fun is very important to me.)

Gifts:

Story teller (I've published stories in magazines before and I grew up with stories)


Faults:

Very Easily confused. (Numbers make me stutter and have issues).

I react better to Knaight's  "Resolution" than Paul's "Depth" in a description of the precision with which a RPG (or any game) defines (and, to some extents, limits) what "can be done".   "Detailed" is more like one of the endpoints than a label for the whole characteristic (with the opposite being "Freeform" perhaps), and it is more likely to be mistaken for the volume of details (probably covered by Knaight's System Mechanical Weight) than limitation on play options.  The "resolution" of a device is the finest level of measurement or action that can be performed; you can see/do nothing smaller.  It is not the volume of details that defines the Resolution of a game, but the degree to which those details (however many or few) are the complete set of choices available.   The more the degree to which you can "play between the lines" increases,  ther lower the Resolution (in the games rules).  [However, JonathanS223 has demonstrated the use of "resolution" to refer to how easy-difficult it is "to come the a solution" rather than Knaight's degree of graininess (fineness of division (or as he said sometimes it is used to imply coarseness)).  Maybe "Rule Precision" is a less easily mingled term than "Resolution".]

Checkers and chess are games with very precisely defined rules for what pieces there are, their starting positions, and what their allowed moves are (Resolution=Legendary; System Mechanical Weight=Poor to Terrible).  You can still play a very complex game with that small but precise set of rules.  Throw a die into a Fairy Chess game where the roll tells you how the chosen piece may move (Rook, Knight, Bishop, Queen, Pawn, or create your own only move of up to three unobstructed squares) and you begin the make a heavier rule set but diminish the amount of predetermination of options (but not much really).

The whole universe of RPG has moved away from that level of control of the allowable pieces and moves.  But D&D in the 70s had a lot of predefined precision (or, in other words, choices limited by rules; you can be a fighter, thief, cleric, or mage; human, elf, dwarf) compared to relatively open-range of Fudge (and later AD&D even).  I have the impression, Paul, that you are aiming at comparing Fudge-based adventures/rulesets (and GMs) versus others in the Fudge genre, not necessarily setting Fudge next to GURPS, AD&D, etc.  Maybe extending to all of RPG (or all gaming) will require the application of your favorite Scale attribute.

So, I started this topic as an intellectual curiosity. One of the reasons FUDGE appeals to me more than any other game/rule system I have every read, tried, or used (and over 35 years of role-playing that is a LOT of systems) is that the code mechanics of FUDGE can be applied to anything. It is remarkably versatile - more than anything else I am aware of. My curiosity drove pondering could FUDGE describe a set of character traits for game systems. Initially, I think that was "FUDGE-derived" game systems. Then it was "game systems". Then it was "game systems or play style".

I still maintain that preferred play style self-selects the game system people choose - and I think our two example so far illustrate that.

I also see your argument Vermonster that Resolution is perhaps a better choice than my suggestions. I also have to add that I love that Jonathan added "Gifts" and "Faults" for GM style. It makes me amused to consider gifts and faults for game systems. Gift: Great Artwork; Fault: No Index!

So for game system so far (combining suggestions) we have:
Reliance upon GM judgment (Knaight)
Overall Resolution (Similar to the term used for optics, as opposed to graininess, which somehow managed to get two completely opposite definitions) (Knaight)
System Mechanical Weight (A measure of rules quantity, basically how mechanically heavy the game is) (Knaight)
Setting Reliance (A measure of how poorly the game can model other settings) (Knaight)
Character Mechanical Weight (A measure of mechanics attached to a character, similar to system weight).  (Knaight)
Rule: (from JonathanS's example)
Mechanics (Vermonster)
Character Creation (Vermonster)
Game Objective (Vermonster) (story telling vs goal acheivement)

It seems clear that Character Mechanical Weight/Character Creation is a consistent choice. Mechanics and System Mechanical Weight seem equivalent as well. Jonathan - was "Rule" in your example intended to the the equivalent of GM Judgment in Knaight's example?