I'm more of a gameplay person. Games can have good gameplay without story but not the other way around. Some games would have still been good if it didn't have and epic story, say Gradius or Doom.
One game I feel is significant proof of this is Portal. Gameplay, Story, Graphics, Art, Sound are the main parameters I look at when it comes to games. I'm not going to lie, I didn't like any other aspect. Story wise I had to put the game on mute because GLaDOS got annoying, the sounds are the same as Half-Life with hardly any music, and almost every room has the same white tiled scheme until you near the end. What am I trying to say? Gameplay alone made the game soar high into my personal favorites! It was probably my favorite game of 2007! Gameplay alone can make a game incredibly fun. Portal was fun, innovating, repayable)(beat it 6 times)and a bunch of other nice words.
I also played Indigo Prophecy, which is the most cinematic game. A game generally has to be really bad for me to hate it, and this was on the verge. Some of the control's didn't make any sense, such as playing Simon Says while being interrogated by the police. Something like that makes it harder to pay attention. Story dominance just doesn't seem to work. I do like good story but that's why I watch movie's and read a books.
Don't get me wrong, story does spice up the game, but if story's the spice then gameplay is the actual meal.
also...
John Carmack said:
Story in a game is like a story in a porn movie. It's expected to be there, but it's not that important