There are fairly comprehensive measurements from 2019:

https://jbp.io/2019/07/01/rustls-vs-openssl-performance.html

I'm pretty sure current versions of rustls are faster than the ones from 2019, but I don't have an intuition for how OpenSSL performance has evolved in the past three years.

I'd like to do another comparison some time soon.

(Yes, the underlying ring crypto library should take advantages of specific instructions available on common CPU architectures.)