I can do both, pending on the style of game.

For RPG's, I prefer having a good, engaging story than the best gameplay-system ever created. I treat a lot of RPG's like interactive movies, really, which is generally why I don't mind a poor gameplay system. (It's also why I figure I have absolutely no issues with FFXIII when tons of others absolutely abhor the gameplay system).

For FPS titles, or 3PS titles, I don't care about the story. I rarely even play the campaign in these games anyway, and just jump into the multiplayer. COD, which I used to play, was enjoyable for the online interaction and not their horrific storylines. Homefront, for instance, has a great gameplay system (IMO) with incredible balance and a better than average story for a FPS title, but the story doesn't hold much of a candle to many other titles. (Like... just about any FF title, for example) but I find it enjoyable regardless.