I recently snapped up last years Muse CD The Resistance and can now say from experience that it is a killer album. The British trio I thought sounded like Radiohead with a more proggy side at first so I was OK with them just not a huge fan. After seeing the video for the title song my perspective changed , suddenly everything they did clicked with me. That led me to buying their album.
And yes, there are bits of Radiohead in the Muse sound with the yearning, quavery lead vocals and wall of guitars approach. Where Muse differs is a willingness to go for the BIG STATEMENT, the GRAND GESTURE. Muse plays towards a more anthemic sound, where the music surges and vocals get heroic. And a progressive / classic rock influence helps pump up the volume louder with flashes of Queen and Bowie to boot. The last three songs are a suite in the grand tradition of prog with the title "Exogenesis: Symphony Part etc" (complete with orchestra) for each title.
Other than the Radiohead / U2 styled rocker "Resistance", my favorite track is "Undisclosed Desires" which is a slow song reminiscent of Depeche Mode in style. Sort of like "Shake The Disease" in style but not melody.
Lyrically, The Resistance puts me in a slightly Nine Inch Nails mood with it's paranoic outlook of being controlled by THE MAN. And being real angry and sad about it. Interesting in that it presents a world where governments keep people in line through meaningless wars and distractions to keep them from realizing that no matter what country they live in, the general population is in the same boat of control and ignorance.
With all these reference points it may seem like Muse is a hodge podge of other bands, what they do successfully is blend their influences into something unique and identifiable for them. The Resistance is the best album I've heard in a while, if it wasn't for W.E.T. I'd say the best in a year. Don't resist The Resistance, because resistance is futile.