Nicely said, good sir! Yes, I admit the question I asked is kinda fundamentally flawed.. "Competition" isn't the right word.. Well, this is my first thread, so forgive me.. The wait for something new from LP is making me restless! And yeah, I said "early albums" of Muse.. I agree that they don't even sound remotely close to Radiohead now (Hell, even Radiohead doesn't sound like Radiohead nowadays!) .. EDIT - It would be one of the funniest moments in rock history if Brad Delson attempted a Muse guitar solo, or even a riff!
Much like Deftones and Incubus, LP is unique and doesn't fit a certain mold. Heck even my friend Steve who hates LP has said that.
I would say everybody. Linkin Park evolved over the years and they do not have a specific genre. Maybe in the days of Hybrid Theory you can call them "nu-metal" or "rock" but now, it's totally different. They are a genre of their own and having said that, they compete with everyone from different genres, I think.