In my experience from working with both, you are much better off with Panda Bullet. I found Panda’s ODE wrapping to be very buggy and incomplete and without a maintainer the situation will not quickly improve.
Also, from what I have read the Bullet Physics library itself may be objectively better than Open Dynamics with a wider feature set and improved performance of some collision types (like between collisions of triangle mesh shapes attached to rigid or dynamic bodies, thanks to GImpact).
I would even go so far as to say it could be a good idea for a future version of Panda to deprecate it’s support for ODE and replace its extremely limited internal physics engine with Bullet as its default physics library (although this might take some doing).