Here's my view:
Palmtree Panic:
Present - Japanese wins. The Jap version is much more exciting, the US version gets kind of dull after a while.
Good F - American wins. The Jap version sounds too much like the present music.
Bad F - Japanese wins. The US version is very dark but the Jap version is more fun to listen to.
Collision Chaos:
Present - Japanese wins. It's much more exciting than the US version.
Good F - Japanese wins. Both are very close, but I'd have to say that the Jap version is better.
Bad F - American wins. The Jap version just isn't evil enough.
Tidal Tempest:
Present - Tied. Both are quite good, and I can't really judge who's better.
Good F - American wins. It's very atmospheric, while the Japanese version again sounds too much like the Present song.
Bad F - American wins. The US version of this track is one of my favorites, with the vocals gasping for air and everything. The Japanese one just sounds crappy.
Quartz Quadrant:
Present - Japanese wins. There's just that one part of the song that I really like which sounds so fresh every time I hear it.
Good F - American wins. The Jap version is pretty good but once again is too much like Present. The American version is really good sounding and I love the atmosphere. One of my favorites.
Bad F - American wins. Again, this version is really atmospheric which I like. The Jap version isn't real good.
Wacky Workbench:
Present - Tied. They are both fun to listen to, and have their ups and downs.
Good F - Japanese wins. Both are pretty close, but I prefer the Jap version.
Bad F - Tied. The US version is nice and makes the place sound dark and lonely. The Jap version is surprisingly evil and has a nice tune to it.
Stardust Speedway:
Present - Japanese wins. Both suck, but I prefer the Jap version.
Good F - American wins. The Japanese version sounds quite nice, but the US version is much more fitting of the race against Metal Sonic.
Bad F - American wins. The US version is very good. The Jap version is very bad. Need I say more?
Metallic Madness:
Present - American wins. Close, but I pick US because of the part near the end, and because I don't care much for Eggman's rapping (Except in the boss music).
Bad F - Japanese wins. Again, pretty close, but this time the Jap version is actually quite evil.
Good F - Japanese wins. It's much, much better than the US version. It's probably one of the best, if not THE best song in the soundtrack. I even switched the order of the Good F and Bad F categories to save this for last.
Conclusion:
Who wins? Neither. Both have their ups and downs. The US version has some atmospheric-sounding tunes which have found their way into my heart when I was young, and the Japanese tracks are fresh and kind of catchy. I actually listen to a mixed soundtrack when I play the game, because of this.