Causes of different behaviour in MJX and CPU MuJoCo

I've been taking a look at MJX, and I'm impressed with how smooth the usage is. As I've been playing around more with the tutorial code on my system, I noticed how e.g. a humanoid running policy that performs great in MJX usually ends up failing eventually when transferred to CPU MuJoCo.

https://github.com/google-deepmind/mujoco/assets/41113387/a078013a-3f1c-445a-9bc8-231b91509286

(video from the "MJX Policy in MuJoCo" cell of the [tutorial](https://colab.research.google.com/github/google-deepmind/mujoco/blob/main/mjx/tutorial.ipynb), with `rng = jax.random.PRNGKey(2)`)

This is of course not too unexpected, considering that I didn't use any domain randomization or other methods that would help with sim2sim transfer. I'm aware of this discussion about FP precision differences between MJX and regular MuJoCo: #1203. Beyond FP precision, are there other key differences in the two versions of the engine that can cause a failure to transfer policies (provided only [features](https://mujoco.readthedocs.io/en/stable/mjx.html#feature-parity) that are officially supported in both versions are used)? Are there certain settings that can be used with CPU MuJoCo to make it behave closer to MJX (or vice versa)?