I don't think there's much of a difference here. Compare these two scenarios.
GM: "Are you going to shoot the guy?"
Player: "Yeah, OK, why not."
GM: "Go for it!"
Player: "OK, I'll use my pistol. I've got slug 2 and a Dex bonus of 1, but the pistol's just been run over, what's that going to do?"
GM: "Well the tires have mangled the sights somewhat....I recon you're at a -2."
Player: "No way! It's not that hard to point and shoot a pistol at someone, I'd say it's a -1."
GM: "Nope, sorry, it's -2."
Player: "OK, OK. So ermmm that's 2 + 1 -2, gives me a +1 overall so that will be a 7 or better."
Rolls dice.
GM: "Are you going to shoot the guy?"
Player: "Yeah, OK, why not."
GM: "Go for it!"
Player: "OK, I'll use my pistol. I've got slug 2 and a Dex bonus of 1, but the pistol's just been run over, what's that going to do?"
GM: "Well the tires have mangled the sights somewhat....I recon it will be a difficult shot now, so that's a 10 or better."
Player: "OK. So ermmm that's 2 + 1, gives me a +3 overall so that will be a 7 or better."
Rolls dice.
If anything, having a descriptive difficulty system makes the evaluation and defense of a target number easier than the less intuitive plucking a DM number out of the air.