I think people forget Thom Yorke can sing normally as well, and does so on a number of songs. When you're the poster-boy for alienation and discontent though, you've got to have a certain style. No one bats an eyelid when Jonny plays contrary to key, but when Thom sings in microtones people get offended. He does have a high range for a male, but he's a small guy, that's the way of things. The beauty of Thom's voice is that there is no discernible gap between his normal and falsetto ranges. He slides all the way up without any change in tone. Sure, it's not a unique ability, but it still sounds awesome.
You can't really compare the two bands or their singers objectively because art is inherently subjective, and they are approaching different aspects of music from different perspectives. Tool have done amazing things for prog rock, while Radiohead gave alt rock some credibility in the 90s and continue to push forwards through modernism. Battles juxtapose modernism and post modernism, and I love them for it. You really have to see it live to appreciate the simultaneous instrument playing and looping shit they do.