I got my game which uses bullet physics to work on iOS with no problems (at least, working as far as the simulator, never quite got around to getting it on a device).

It's been many, many years since I've even tried to use ODE. Bullet is an excellent engine, easily AAA/industry quality and it has shipped with plenty of games. You know you're getting a solid system that can handle almost anything you throw at it. It's getting massive GPU simulation support in the very near future too, which is a big step forward. On almost any technical merit I would choose Bullet without reservation.

What is not so good about Bullet is the documentation. We've had to pour over the source code to understand what's going on and how to use functions.

Getting bullet to work on iOS is super easy. Ignore the instructions they give.

1) Create a new XCode iOS static library project and empty it out.

2) Add the entire bullet source tree.

3) You'll need to remove some CMake files manually, or XCode will complain about not knowing what they're for. There's also a few other things to skip like MiniCL, ibmsdk, etc.

4) Link it to your application like any XCode static library project.

I've never bothered with CMake to build bullet.