Earlier quoted context omitted.
They key difference is with mTLS approach you'd have to steal the private key of the client certificate if you want to impersonate the client. In most secure deployments of mTLS and short lived certs, private key never escapes the TPM, Secure enclave or Yubikey, so it's extremely hard to mount an attack and impersonate a service. With JWT (assuming it's not bound) you can steal JWT token and re-use it until it expire…
I still don't get the difference. If someone steals your secrets you're screwed. No matter what kind of secrets that are. That's clear. But if you keep your secrets in a HSM (TPM, SmartCard, …) and only use them to derive session keys directly on the secure device there is absolutely no difference which concrete tech you're using (given that secure cryptography is in place). mTLS is a great approach, no question. But…
I wish there were "real" standards and a better ecosystem for request signing.