I think everyone will be surprised that I voted for Floyd. Crimson's one of my favorite groups ever, but objectively, Floyd's output - as a whole - is superior, if only for the consistency. Crimson, it could be said, gets points for longevity, diversity of style, and sheer volume of output, but that could also be interpreted as being stretched too thin and unfocused, and realistically, I don't care for anything Crimson's put out this decade, and they haven't really been truly relevant since the '70s anyway.
I don't think it's an entirely fair comparison in general though, as they're really completely different animals (
dogs and pigs?
sorry... ) Crimson is far more aggressive, energetic and unabashedly edgy, while Floyd is more cerebral, atmospheric, and ultimately accessible...although I suppose we can call both groups "Art Rock" if we must. I think the real test is that, on a direct album-to-album comparison, Floyd's output has the more consistent quality -- the only real competition Crimson brought to the table while they were both active was in 1973 w/ both Larks' Tongues in Aspic and Dark Side of the Moon seeing release, arguably the best albums from both artists.
I love both bands, and in general I prefer Crimson as a matter of personal taste (and in terms of pure musicianship, Crimson's always been technically superior), but overall, I would say Floyd was better in terms of creativity, overall quality and songcraft...after all, they had a pretty substantial head start w/ Piper At The Gates...a record that was in itself more innovative than just about anything Crimson recorded.