I'm pretty sure I read somewhere that Satriani was Steve Vai's teacher. I like Satriani better, to the extent that I know his work. His material just seems more appealing to me, more overall-musical. I reviewed his Flying in a Blue Dream album several years ago, and am still of more or less the same opinion. Here's something from that album, "The Forgotten."
I don't know what album this song--"Always With Me, Always With You"--is from, but it must be an earlier one, because he looks pretty young, and not bald. For some years now he's always appeared with a shaved head, or occasionally a stocking cap, which I take to be his solution for the problem of balding. Anyway, it's pretty, and also includes a very expressive solo. And it's a pretty video.
Something more recent:
My memory is really getting bad. I was thinking, after having featured Eric Johnson, Steve Vai, and Joe Satriani in this series, that I would close it out with something from G3, which is a trio of guitar heroes featuring Satriani and a varying list of others. So I looked on YouTube, and I didn't find much featuring the Johnson/Vai lineup. This is one of the few. "Red House" is a blues, well-known to Hendrix fans (Johnson starts it off with Hendrix's riff). So I set up the link here. And then when I searched the blog for Satriani's name so that I could link to my old review above, I discovered I'd already posted this, and only six months ago. Well, here it is again.
Whose solo do you like best? I like Vai's a whole lot. Maybe the limits of the blues kind of kept him a bit more down to earth.