The greatest band of our generation is Tool (see here for most epic, inspiring and beautfiul piece of music of my lifetime:
http://www.youtube.com/watch?v=EDlC7oG_2W4, although its almost a shame to hear it seperated from the rest of the album). Close behind are NIN, a band exploring the full spectrum of human feeling to a greater degree than any other I can think of whilst just rocking the **** out of everyone.
But Radiohead are definitely worthy of big consideration.
The sheer diversity of their portfolio puts nearly all other bands in the shade and yet the quality remained just as high. As a testament to that fact I am sure most hardcore Radiohead fans would list Kid A as the best Radiohead album or at least close if its not their personal favourite, despite it being electronica and completely removed from anything they had done before or anything in the mainstream music industry.
If you don't personally like the band thats fine, but you can't deny that they need to be heavily considered in a discussion of this topic and that is the most you can say about any band. If you try to argue otherwise then you are going to look foolish imo. Almost as foolish as if you try to claim Modest mouse are the best band of our time.