Nitpick: Remote code execution is breaking a TLS implementation (eg. openssl), not breaking TLS itself.
> so I'm assuming the difference here is that it's the CPU management chip instead of your browser?
Yes.
If a vulnerability is found in a SSL/TLS implementation, it can be fixed with a software update.
I don't know how Intel ME works, but I'm guessing updating it is harder to update than a browser.
> For that matter, do you trust SSL/TLS significantly less than SSH?
I'm not the GP, but I'm guessing they do. TLS solves a more complex problem than SSH, as SSH assumes the user validates a server's public key manually (even though they usually don't, but TOFU [1] makes it somewhat harder to exploit), whereas a TLS server's key can change at any time.
[1] https://en.wikipedia.org/wiki/Trust_on_first_use