I would definately get the LP2 over the Mixr headphones. They are both stylish and very portable. I know the Beats Mixr has excellent isolation due to it's high clamping force which is good and bad because you don't want headphones that will end up hurting your head. I'm not sure about the V-moda on isolation and comfort but V-moda headphones are built like tanks. The Mixr's are a mainly plastic build and the pair I had, the headband snapped in half from putting it on my head.
I also have the ATH-M50 and those isolate pretty well, have a pretty solid build, and the cord is long. They are not as portable as they are more intended for studio use. I think all 3 of those headphones have emphasized bass and are tuned for more of a fun sound with the ATH-M50 being the most neutral of them all (though still bassy).