I believe that when it come to the appeal of video games, there are two categories that generally separates what we want, and what we expect from them. We're either looking for a challenge: something to test our might. Or, we're looking for an intriguing experience.
Now, of course, this is my opinion - there can be dozens or over hundreds of other factors involved - but, right now, just play with me...
Basically, when you're looking for a challenge, you might be playing a online match, a fighting game, or a game on the hardest difficulty setting. Story or exploration doesn't concern you, and it's all about the gameplay and its fluidity, or variety of options you can engage an opponent.
Now, with exploration, the focus can be the story, or the sheer experience of it all. You like to side quest and veer away from the obvious path (sandbox). A lot of times, you're looking for something unique and innovative. Gameplay doesn't come down to how well you completed a mission (or, if you were able to at all), but what you did to get there.
So, what would you guys prefer?
Personally, I would probably choose both. But if I had to choose one, I'd go with a challenge.