In Phudge I give a base damage level to broad types of weapon and then the relative degree shifts that up.

e.g. A small pistol does Mediocre damage (2 in Vanilla Fudge) and then is shifted up by the relative degree

My personal preference when playing Fudge is to use the weapon's Offensive Damage Factor (ODF) modified by the relative degree of success in figuring out damage. This is regardless of my use of "objective" or "subjective" action resolution.... If I'm "just fudging it" and not using the objective damage factors etc., I'll consider both the weapon and the degree of success in describing the results.

Paul and I also play D&D (specifically BECMI / Rules Cyclopedia rules). There, degree of success doesn't really factor in... and the weapon's damage is random.

So you can think of Fudge as flipping those around: weapon damage is steady, degree of success makes the difference.

Does that help?

I have been fiddling around with this some lately, and I finally came back around, full circle to degree of difference as damage result. Like others who've responded, I use a base weapon damage, factored into the ODF, and take it from there. It does kind of feel like Classic Traveller sometimes with the modifiers.... you add this, subtract that, mumble, mumble, mumble... to come up with a +2 or something, but I really feel like that kind of abstraction is simple, and smooth. Gives you a "realistic" chance after everything is factored in. I also like that we call them "factors" in FU, because it inspires players to think of all of the factors that might contribute to a given situation, sort of the way we do IRL.

Oh, and also, after MUCH twiddling around, I still can't decide if I like opposed rolls for ranged attacks, or using an attribute+factors as a target #. Right now the balance has tipped in favor of opposed rolls again, but I am considering changing it back for two reasons. 1. It makes ranged and melee attacks FEEL different, and 2. I feel like it's more deadly, as a gun should be.
On the other hand, I like the opposed rolls, because like in GURPS, it is fun for players to be on the defensive and get to roll opposed rolls, rather than just sit there, taking it on the chin until their turn.
One idea I am toying with is using 4dF+d10 system for ranged attack-opposed rolls, and the usual 4df for melee. That way both sides get to attack and defend actively... I just have to figure out how I want to calculate degree of difference, but it wouldn't be difficult. There is an article here somewhere that describes this.

I find that it does help me using the ODF and DDF along the lines of my players telling what weapons are better for upgrading. I converting my player group from D20 to Fudge so I like to keep some of these modifiers to give them something familiar to latch on.

I, personally, like the ODF and DDF as it gives a bit more for players to work with than just story.