This is my short comparison between Box2D and Nape. I’ve used Box2D AS3, and then Box2D Alchemy for a year or so. I’ve spent a lot of time hacking through it, so I feel that I’m qualified to make this comparison. The thing you need to ask yourself is this: “Do I want more speed/performance, or do I want accuracy in my physics simulations?”
EDIT: Deltaluca has been helping me with my game, and I have been testing his new version of Nape, which is faster, stronger, better. He plans to tackle CCD, and has introduced island sleeping. The old sleeping will be implemented at some point in the future. The problems I was having with strange sleeping and other odd behaviors in Nape came from my use of a physics scale, something often used with Box2D. I can now say with confidence that Nape is the best choice for physics in Flash.
EDIT AGAIN: Deltaluca has been making a lot of progress on newnape (name pending?), and has added constraints and a lot of other things you should check out! The review below isn’t terribly outdated, but I’ll probably review both newnape and box2d after some more updates/milestones are completed.