Depends by the type of game.
I mostly go with the storyline , i have tried some games that they can run even on my calculator but that can annihilate the story of some of the modern day games. The game must have a good plot or an objective in case of games that dont require a plot to attract the player and immerse him in the game's world. In few words to make him forget about the graphics , or the outside world. Thats a true game.
But why it depends by the type of game?
Some games requires good graphics to create the games atmosphere, like the right darkness, fog, particle, combined with the sound effect , like Amnesia or even the latest P.T Sillent Hills game , the graphics made that game 10x scarier and the sound ...oh god...
So my point is everything depends by the game.
And the war between the "graphics fanboys" and "oldschool fanboys" is totally bullshit.
Edit: My explanations have been short and a bit messy/confusing these days as im going on a lot of stuff like moving house , preparing for university. Also a small brain meltdown but well.... thats normal aye? Lets grab a beer and drink it off...