I think it all depends on the individual. I have a liking for indie music. :) Personally, I love the New Moon Soundtrack a little much more than the Twilight Soundtrack.
Those who prefer mainstream music would probably prefer the Twilight Soundtrack than the New Moon Soundtrack, since you have Decode, I Caught Myself, Leave Out All The Rest, etc.
Indie music lovers would probably love the New Moon Soundtrack. Done All Wrong and Satellite Heart are my favourites off the New Moon Soundtrack. :P
Don't get me wrong. I LOVE the Twilight Soundtrack. I'm a HUGE Paramore fan- heart and soul. x) It's just that I've recently discovered that I love indie music. Like I said earlier, it all depends on the individual.
Well, I did really like the Twilight soundtrack, and I only listened a little bit to the New Moon soundtrack. So for now, Twilight one :)
But there was this one song that I truly loved on the New Moon soundtrack; the music from the part where Jacob (and I think other werewolves) were chasing Victoria after she almost killed Harry Clearwater.