Grohl is certainly the most broadly talented. But seeing as how music is subjective, and I never really got jazzed over Nirvana or Foo Fighters, I have to go with a tie between Chris Cornell and Jerry Cantrell.
That whole period of time was blacked out for me; it was early in my professional career, and i had a young family, so I didn't listen to a lot of music and didn't keep up with whatever new was coming out. A while after that, a friend gave me one of his Soundgarden CDs, and I took it home and listened to it. It blew my mind. I could not get over how great Cornell's vocal sounded, and I loved the guitar riffs. I found AIC much, much later. In fact I just saw Jerry Cantrell with his band open for Bush a few weeks ago.