Neither. Bose are better than Beats but both are very overpriced; it's all just branding. Beats are basically slightly better iPod headphones with the bass turned way up, and the bass isn't even quality, it's muddy and distorted. They are probably the equivalent of $50 headphones. I haven't used Bose before but apparently they're good, just overpriced.
I use Denon AH-D2000's which are cheaper than or equal to Beats and Bose headphones but are far superior. You can't go wrong with Sennheiser's or ATH-M50's either. And then if you match any of those headphones with a good amp, you have sound quality that blows your mind 2x.