I need a physics engine that features a constraint solver, and sophisticated joints (ball joint, hinge joint, universal joint, etc.). Ode contains exactly the features I need. I went over all the documentation and some example code, and it seems perfect. But then I started reading about Bullet and it appears that it features some pretty sophisticated joints and a constraint solver too, and is more robust and widely used. So I'm trying to weigh which would be a better decision.

Pros for ODE:
1. Smaller, more lightweight and specific to my needs.
2. Im already familiar with it.

Pros for Bullet:
1. More widely used. (i.e. skills are transferable to other projects, easier to obtain help and tutorials online)
2. More stable/better maintained (Ode seems to be buggy. Some of ODE's prepackaged demo's crash occasionally)

Any oppinions or input (especially from people who have used ODE) would be appreciated!

I think you're biased to ODE. No problem since you're already familiar with it.
My main concern with ODE is that it seems to be falling out of vogue while Bullet is apparently taking more and more momentum.
Keep in mind that a lot of Bullet source involves demonstrations of various functionality. To this regard, it's rather well documented (albeit the official docs are a bit rough).

As far as I know both Bullet and ODE took various features from each other. The original ODE solver was more accurate and ported to Bullet. At the same time, it is my understanding the faster Bullet solver was ported to ODE as well.

Haha, yeah I may be a bit biased to ODE, but only because I went over it and I know it has all the features I need. Bullet is still unknown to me. Also I found the ODE documentation and example code extremely comprehensive and easy to follow (mind you I already knew a fair bit about physics engines, so that helped).But as you say, Bulet is way more popular, and I'd wager, more stable. I think it might be worth investing the time to learn.