The quick version:
What games have used the difference between the "attacker" and "defender" actions to resolve the damage or tilt the stakes?  Were there pitfalls to this approach?

The long version: 
The game I'm designing uses a fairly straightforward mechanic:
2d6+(Character's Stat)+(Circumstances) vs. Target and NPCs "roll 7" so the dice are all in the players hands. 

In the olden days, we used what I then called "descriptive damage" - if a PC beat the opponent by a large margin, this would be a big success (i.e. "You decapitate the wyvern!).  By a small margin, it would be a small success ("You slash at the wyvern's flank, it cries out!")  But this required a great deal of trust on my players' part - that I'd be consistent and fair with this.  What I'm trying to do is write less arbitrary rules but still capture what we were doing at the table - basically, Players Action - Target for this situation = Degree of Success.  I can't think of any games that do this (Unisystem's success levels are based on the same level every time, which causes that big blowthrough) and I'm wondering if there's some inherent problem I'm overlooking.  I know some people hate subtracting but I figure if the GM doesn't have any dice, that quick math can be the GM's job.

Unless I'm misunderstanding what you're talking about, it seems to me that a lot of systems already incorporate the sort of mechanic you've mentioned: White Wolf games, Godlike, Shadowrun - and almost anything else that uses a comparison of hits or successes.

I don't know that there are any pitfalls as such to using this kind of mechanic; it would depend on the kind of game in which the mechanic is embedded and the kind of conflict to be resolved.

Shadow of Yesterday and Spirit of the Century (both of which are available free under the open gaming license) might be games for you to look at.

In fact, Shadow of Yesterday v1.0 started out as 2d6 vs 2d6; v2.0 now uses FUDGE dice like SoTC.

Yeah, I hadn't thought of it in terms of success levels vs. success levels in White Wolf games.  I actually have never played any; but do those games use "My successes - Your successes = Result" or is it more "If my successes > your successes, I win, else, you win"

Is Version 1.0 of TSoY available anywhere?

White Wolf used to use contested rolls more often.  For combat lately, they've been tending to use defense values rather than opposed rolls.  In any case, margin of success tends to matter in White Wolf.  And this is equal to Attacker - Defender, thus a difference equation, with similar equations used for other types of opposed or extended rolls.  With unopposed rolls, though, margin of success sometimes is meaningless.

Soak values, used in some WW games, add another layer of complexity, because you really have to have two difference equations in combat.  Considering combat is a time when many actions are being taken, it would seem like the worst time to bog equations down with extra math and extra rolls, but here it is:

Roll Attribute + Ability + Weapon Accuracy to get Attacker Successes
Defender successes/defense value is either rolled, or roughly half of Attribute + Ability

Margin of Success of attack = (Attacker Successes) - (Defender Successes/Defense Value)
If MoS of Attack > 0, attacker hits defender.
    Add MoS + Weapon Damage - Defender Soak (difference), and roll these dice to determine how much damage was done.

So, as you can see, this takes up to 3 rolls.  Without soak and with defense value (new World of Darkness), Defense becomes equal to an Attribute, and simply subtracts (again, difference) dice from the initial attack pool.  Damage occurs in the same roll.  Soak is taken care of just by basing someone's "hp" off of Stamina instead of fudging around with numbers during play.  Now it's down to one roll, still using difference (but only once).

-Jason T.

Simple 20 (http://miscellaneousdebris.sitesled.com/games.html) uses the difference a in combat: if the attacker scores higher than the defender, the damage is the difference. It doesn't work the other way though: if the defender wins, the result is that they've dodged or parried, regardless of what the difference was.

It's a commonly suggested rule for Fighting Fantasy that it should use the difference in combat as well. In the official rules, both players roll 2 dice and add their Skill, with the loser taking a set amount of damage. The common suggestion is that the loser should take damage equal to the difference.

By way of an informational plug, I use the difference between opposed rolls to partially determine the degree of success or failure in my game-in-development, Silent. Here's how it works.

If the total rolls are the same on both sides, then it's a tie.

If the attacker wins, his MoS is added to his weapon's (static) damage value. Just one roll, thank you.

If the defender wins, his MoS is added as a bonus to any plausible action in the next round against that opponent; he's jockeyed for position or somehow put himself in an advantageous position relative to his attacker.

The system has playtested well so far and manages to keep things moving, while simultaneously keeping defense a desirable action (save up that defensive bonus for a huge attack later on, when your enemy is severely out-maneuvered).

Passages uses the sort of system you are talking about. On a successful attack, the difference between the result of the attacker's check and the defender's check is the base damage (which is further modified by the damage modifier of the weapon). It also works this way for, say, getting struck by lightning. In which case, on a failed check (similar to a saving throw), the damage from the lightning is equal to the difference as modified by the lightning's damage modifier. It works great, IMHO.