I had a pair of Powerbeats 2 wireless earbuds for a week before returning them. They went back to the store as they just would not stay in my ears despite having the over-the-ear hook. The sound quality of the two are pretty comparable. Both are bass heavy but the Bose have a better sound stage. Instruments can play in the very far left or right of your ears instead of sounding like they are playing in the center of your head. It's something that nice over-the-ear, full sized headphones can do but not very many earbuds. I also preferred the level of highs in the Bose as they didn't sound too harsh. The Beats have more of an accented V-shaped sound signature in that the lows and highs are boosted but the mids taken down. The Bose have a similar sound signature but their highs aren't as harsh and the mids come through a bit more.
I would hold off on buying any Beats product though. They have all been on sale recently indicating that Beats (actually Apple) is going to update them soon to newer models. You can either go with the Bose now or wait a bit (closer to the end of the year) and see what Beats does. Personally though, Bose has always made better earbuds than Beats. I h ave always preferred their SoundSport wired earbuds compared to the Beats Tour earbuds.