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Looking at three comments on how dice pools differ from dice + mods, I see one point in common: feel. It just feels different to hold a nice big handful of dice, and I can fully understand the tactile appeal of combat factors affecting the dice in your hand, not just an abstract number in your head. A couple of the comments also mention that shifting pool size and target numbers create probabilities more difficult to compute than an unvarying number of dice + mods. I can see how that might help keep number-crunching players more focused on play than on probabilities. 

kenclary also notes that in TRoS, the dice pool effectively doubles as an action point scheme. Good point. 

Blizzard notes that more dice means a change in the probability distribution, something that's true and needs to be considered by a designer. Although in the case of dice pool mechanics, I'm thinking that it's an unintended effect, or possibly even a very minor negative side-effect. That is, I assume designers fully expect and want a pool of 10 dice (lots of bonuses!) to on average yield 5 times the successes of a pool of 2 dice (lots of penalties!), but I don't assume that the designers necessarily want the 10-die pool to yield a very tightly-clustered number of successes that rarely stray far from average, and the 2-die pool to deviate more freely from its average. (In the same way, I don't think RPG designers are looking for the effect that typical 1d sword damage is just as likely to deal max dam, min dam, or any dam in between, while a powerful 6d weapon will strongly cluster around average dam. That's just the way things work out.) Then again, maybe some designers do have reasons for liking the way a changing dice pool affects both average successes and deviation from average. I don't know; it's pretty harmless either way.

Anyway, getting to my key reaction to the comments, it's this: I was actually expecting that there was some more purely mechanical benefit to the dice pool system. That is, I had some expectation that compared to the conventional dice + mods method, which yields both a) success/failure result; and b) degree of success/failure with a single roll, the dice pool method with its added dimension might yield a) success/failure result, b) degree of success/failure, and c)... something else, which I've been overlooking. Maybe that's not the case? 

Well, even if there isn't an added benefit to dice pools in terms of crunchy useful results returned, or other ability to do tricks that dice + mods can't, the points about fun and feel are well-taken. Lots of dice do make a nice sound. (I was thinking that I've never played a dice pool game, but some HERO mechanics are at least partially dice pool-ish, and where superheroes are concerned, those big handfuls of plastic do feel "right". : ) 

Thanks to all for the comments and enlightenment!

(@Perrin: "Column shifts"? Actually, I do vaguely recall the mechanism, now that you mention it, though I can't come up with specific games I might have played using it, or even exactly what's involved. Any detail you could add to refresh my memory?)