I prefer a game that has game mechanics. The more immersed I can be in a game, the better. I'll always prefer a sandbox with puzzles, stats, mini-games, management features, currency, etc. Assuming that they have been implemented properly, that is. Don't get me wrong, a well written linear story is great; especially if it has branching paths, multiple endings and interesting characters. But they always feel less like "games" and more like "choose your own adventure" novels.