JAX introduced a lot of cool concepts (e.g. autobatching (vmap), autoparallel (pmap)) and supported a lot of things that PyTorch didn't (e.g. forward mode autodiff).
And at least for my applications (scientific computing), it was much faster (~100x) due to a much better JIT compiler and reduced Python overhead.
...but! PyTorch has worked hard to introduce all of the former, and the recent PyTorch 2 announcement was primarily about a better JIT compiler for PyTorch. (I don't think anyone has done serious non-ML benchmarks for this though, so it remains to be seen how this holds up.)
There are still a few differences. E.g. JAX has a better differential equation solving ecosystem. PyTorch has a better protein language model ecosystem. JAX offers some better power-user features like custom vmap rules. PyTorch probably has a lower barrier to entry.
(FWIW I don't know how either hold up specifically for DSP.)
I'd honestly suggest just trying both; always nice to have a broader selection of tools available.