Note to readers!
This question was originally asked and answered in 2011, but I'll do my best to keep it up to date!
Here's what I've found:
- kripken/box2d.js is a port of Box2D using Emscripten and works well and is fast. I have used this personally with great success.
- planck.js is the newest port and is written from the ground-up in JavaScript
- Box2DJS is a port of Box2DFlash 1.4.3.1. box2dweb is a port of version 2.1a.
- Box2DJS works "as a CommonJS module without any modifications at all" [1]
- Box2DJS "not up-to-date and you have to import a big amount of JavaScript files in every project" [2]
- box2dweb is contained in a single file [2]
- box2dweb is "a much newer port and has a lot fewer issues" than Box2DJS [3]. However, switching might introduce new issues [4].
- Box2DJS depends on Prototype but box2dweb does not [5]
- Seth Ladd has promoted box2dweb with examples on his blog [6]
- Nobody seems to be using the third alternative.
- There are also physics simulators not based on Box2D. Check out Matter.js and p2.js
There's also a similar discussion on gamedev.stackexchange.com.
I'd say that the winner is kripken/box2d.js.
