Joe Satriani is not underrated. In fact, the opposite Guitar World’s greatest you wouldn’t understand shirt may be true. He has made a very good living performing his own particular brand of guitar virtuoso music. In fact, I saw him live in 1990 and felt moderately entertained for most of the time. His own brand of virtuoso music is very much allied with the rock guitar movement from the 1980s and onwards. This is a movement that had little interest in nor influence from Jazz music. Compare Satriani – and perhaps Steve Vai – with the guitar virtuosos of the 1960s and 1970s like Robert Fripp, Jeff Beck, Frank Zappa and John McLaughlin whose playing had been influenced by Jazz and who had all created Jazz and progressive arrangements. This is where I feel Satriani and Vai have tended to repeat themselves rather than explore new themes like some of the 1960s and 1970s originators did.
So Joe Satriani and others like Steve Vai Guitar World’s greatest you wouldn’t understand shirt leave me cold, unfortunately, in that their playing is formed from the much-simplified model of the 1980s which was about speed and prowess of the player and less about the music they are playing. For that reason, I think Satriani is massively overrated! As far as the musicianship is concerned, they are 2 different guitarists, both innovative in their own way. Both exciting, both creative, both respected (including by each other). They have gone in different directions musically, but have a lot of crossovers. So, as I said before, BH is one hell of a shredder. A shredding competition with Satch would be a close thing and might even be down to ho each guitarist feels on the day. Vai and BH would probably be a fairer fight.