I can't pick one element, it is important for me to look at different aspects. Such as whether there is at least one guy that I like among the cast of characters, does the plot have any mystery, what is the gameplay like, is does the art look nice and match the game's vibe.However I also consider myself as quite lenient when it comes to trying things, maybe because the first games I played were small ones that did not look good, yet they give me nostalgia. I am willing to test different games before making a decision to continue.
And for me writing can salvage bad art but not the opposite. It is hard to describe but, with pretty art, the game will inevitably reach a point where I see the same backgrounds and the same character JPGs over and over, the only new art awaiting will be CGs that I have not unlocked, if I get bored I don't care about seeing new CGs anyway. However good writing and good story can still evolve in a game and captures my attention.
But my mood overrides all else. If there is a day I feel like playing a lighthearted game with no plot or pick up something I used to drop, I will.