In my opinion Muse is starting to get bigger here in the US. They're slated to play SNL in December, they got a slot on the VMAs in September I believe, and they're planning an arena tour in the spring. They've headlined Austin City Limits and Lollapalooza, as well as Almost Acoustic Christmas (in 2007, and again this year), all that means they're getting fairly big here.
But again, it all comes down to territory. Muse is having a stadium tour next summer in Spain, Italy, the Netherlands, and the UK (that's all that's been announced so far, anyway). LP is bigger here, yeah, but Muse is far more popular all over Europe.