I have both and like both. The BP is earlier and smoother off the spot. The Anarchy is still smooth and early for a pearl, but more angular than the BP. I don't think you can go wrong with either. I like the Anarchy much better than the Invasion.

Here's my detailed review of the Anarchy. I still really, really like it, but unfortunately I haven't seen as much oil in the front part of the lane the past couple weeks in both leagues and tournaments, and the ball hasn't really been out of my bag much because of the sanded finish I'm using on it. (In fact, I've been throwing a Tropical Heat a lot and even had to switch down to a Mars last night by the end of the night!) It has calmed down a couple boards of overall hook after about a dozen games, but that's the case with basically every single bowling ball I've ever owned, and it's still plenty strong and capable of covering boards if I want it to.

I also reviewed the Anarchy so you can read that for detail. Overall I still love the ball.  Tons of backend and VERY angular.  Like someone said earlier, it does get tamer after a few games, but is still wicked.  I LOVE this ball compared to the Invasion.  Anarchy is the first ball out of the bag.

Balls in the bag and order they come out:
#1-Anarchy #2- Virtual Energy  #3- Virtual Gravity #4- Gravity Shift #5- Big Hit (spare and really dry)
#6- Teal Rhino Pro (oldie but a goodie)