I\'m planning to write a 3D FPS game, based on WebGL.
A few new options emerged since this question was first asked.
For games, Turbulenz is a very good library: http://biz.turbulenz.com/developers
Playcanvas seems to be good too: https://playcanvas.com/
Depending on your needs regarding download size, Unity can be a good choice too. With it, you can export your game to almost any platform. The only downside maybe is the relatively large files it produces. http://docs.unity3d.com/Manual/webgl-gettingstarted.html