To me it's Joe Satriani without question. First it's the music. Joe has expressed such a wide range of styles in his work. I just don't see Steve Vai doing that. Joe can go from the stark but deeply melodic Rubina to shredding so intricate you just put on some shades and watch the notes go by. He does fast, slow, very melodic, hard screaming shredding, and fun spirited stuff like A Day At The Beach that strikes me as someone happy just to play. My biggest hangup with Vai is I just can't stand his style. His constant use of the whammy bar is like a 14 year old boy who just figured out what his wang is for and just can't keep his hands off the damn thing. I find myself listening to Vai and wondering ok, where's the whammy dives.... ah, there they are, another decently listenable tune wasted. My second argument that leads into my perception of the two is their marketed style. Vai has always struck me as a guitar diva which personally rubs me the wrong way. While this has no measure on his ability to play it colors how I view his work vs. others. Satriani might be a complete jerk to work with (I have no idea) but that doesn't seem to project in his music. When you can do something as goofy as The Phone Call that just doesn't strike me as an egotistical purist where what I've seen and heard of Vai is. To me it's Joe, he can compose and play such a wide span of styles from the simple to the impossible. Vai may be more technical in some aspects but his style, presentation, and constant going for the whammy just strike me as a narrower overall musician than Joe.