I'm talking about a game that specifies a result and then explains it with fluff vs a game where the flavor text is intrinsic to how it works in that world.
That's at least getting into a mechanical distinction. The former is what I've gotten used to (from discussions of Hero System) calling an 'effects based' system. The advantages of such systems are myriad. They use fewer mechanical sub-systems to model the same range of things, they can be expanded with few or no additional mechanics, they can be turned to a variety of genres or tuned to a variety of styles with relative ease. The only disadvantage - and it's a doozy - is the level of abstraction between the mechanic that resolves the effect, and the 'special effect' that causes it to happen. In a mechanical (gamist) sense, what's 'really happening' is the end result effect, and in a narrative or simulation sense, what's 'really happening' is the special effect.
In Hero, for instance, the rules for designing the mechanic are detailed and fairly precise (there's some room for GM-approved hand-waving when it comes to limitation), while the rules for the special effect are prettymuch anything-goes - but /both/ are highly customizeable. The GM, to paint a certain sort of genre or campaign, can always limit what powers are available or what special effects they can be used to model, as well as how powerful ('Active Points') a given power can be. And, there are powers and limitations that work based on special effects, with values the DM bases on how common that special effect will be in his campaign, so you can actually customize the degree of interaction between mechanic and F/X you like - if you've sufficient mastery of the system (and that's another doozy).
4e is not so committedly nor so consistently effects-based as Hero. While they both use the term 'power,' for instance, a Hero power is a building-block that can be customized to the nth degree, while a Hero power is a complete character action that you either choose or don't choose. Conversely, a Hero 'special effect' is chosen when the power is created, and can be have some reference to how it interacts with other (specific) powers and any power with specific limitations, based on how 'common' the DM deems the F/X, while flavor text in 4e is casually mutable and has no bearing on mechanical resolution save by DM fiat overriding the rules. And, outside of powers, Hero remains consistently effects-based (your STR could represent musculature, no-range telekinesis, bionics, power armor, or a magic belt, for instance), while 4e, beyond power and character description, largely drops the concept with respect to stats, skills, and other character abilities.
I can understand people not liking Hero, it's an enormously complex, terribly abstract system , with some odd foibles, and takes, IMX, a year of attempted play to even really grasp, and who knows how long to 'master.' Plus, it has some real problems, from a few broken mechanics that have become enshrined (like the KA 'stun Lotto'), to it's bloated open-ended skill system. I can even understand them not liking it /because/ it's effects-based, because it is so relentlessly effects-based.
4e, I don't see the turn-off so much. The effects-based component (powers) is not that hard to ignore and has little impact on the playability of the game, and it is an easy to pick up, easy to run game that doesn't much punish 'lack of system mastery' early on, while having enough breadth, choice, and customizeability that system mastery inevitably creeps in to hold the interest of the more jaded player (
comme moi).