I've listened to a fair amount of Friedman's solo stuff (apart from some of his recent releases) and they're pretty good. Anyone who likes someone like Satriani (instrumental guitar music) would probably quite like his solo stuff. Although if you like his Megadeth playing try listening to his first album Dragon's Kiss; basically Megadeth without Mustaine singing. Not sure how to word this: like Satch, Friedman does emotion but it's tinged with this cringeworthy, for lack of a better word, cheese. It's just so fucking smootchy sometimes; and this robs it of true emotional impact, for me anyway. Buckethead, while doing stadium-rock-soloing-cheese fairly well, has a deep undercurrent (in much of his work) of heartwrenching pathos; an emotional depth that I genuinely don't hear in quite a lot of other instrumental guitar music e.g. Friedman, Vai, Satch, Malmsteen, Gilbert, Lane, etc etc. Deeply resonates with me anyway. And I know it's hard to imagine for those of you who've just seen videos of Buckethead playing Jordan & shredding etc; but seriously, Buckethead has written some beautiful, haunting music that deserves a wider audience. There's also a rawness & unpolished feel to much of his music which I find refreshing (sometimes) in comparison to most production-heavy Metal/Rock music.
Still, if it's ToS-solo vs. the-guy-who-wears-a-bucket, then there's only one winner really.