Both KMS and CloudHSM are FIPS 140-2 Level 3 and AWS claims they cannot read private keys from KMS. The main difference is KMS uses IAM and the AWS REST API while CloudHMS uses PKCS #11/JCE and a separate permissions system.
My understanding is that AWS KMS uses AWS designed HSMs and are tightly integrated with all AWS services while while CloudHSM uses LiquidSecurity 2 Cloud HSM adapters and use more conventional APIs
>My understanding is that AWS KMS uses AWS designed HSMs
That's my take as well reading about how they handle firmware (sounds like they're using their own chips, presumably similar to how they use other hardware acceleration and offload)
I think the real paranoid people use cloudHSM.