I bought Heavy Rain and rented Alan Wake.
They're two completely different games, but I enjoyed Heavy Rain a lot more. Alan Wake had a pretty good story, but I was bored with the fighting by the second chapter. Hit baddies with light, shoot, repeat. During the last half of the game, I was literally just running away and dodging the cloned axemen because I was so sick of fighting the enemies with the boring combat system.
Heavy Rain's story was also good, and I felt a lot more immersed in it than Alan Wake.
+1 to Rock_Starman saying Deadly Premonition is better than both, though.