First, Joe Satriani didn't teach Vai how to play guitar, he only introduced him to it. They lived by each other when they were growing up.
Second, although I dislike kRiK OmELeT, you gotta give the guy some credit for being a part of a great band and influencing a lot of people's guitar playing.
And my choices are,
Technical ability alone: Shawn Lane (RIP) without a doubt, if you've never heard him, grab his CDs and be prepared to drop your jaw, simply astonishing.
Songwriting, Phrasing, and Replay Value: Steve Vai
Overall: Steve Vai - Awesome technical ability, awesome songwriter and about the only solo guitarist that I can listen to a whole album of without getting bored.
As for the guy who wanted some examples:
Shawn Lane - Not Again
Steve Vai - Tender Surrender, Boston Rain Melody, For the love of God, Giant Balls of Gold, Bad Horsie, Erotic Nightmares, Blue Powder, Jibboom....to name a few.
Sometimes I hit notes only dogs can hear.