Let's suppose that two entities, A and B, are establishing a secure channel and then require a mutual authentication.
A has only a RSA key pair and B has an ECDSA key pair. Both of them trust the public key of each other.
Do you feel comfortable with having A signing it's message with RSA and B signing its message with ECDSA ?
They do have an equivalent key length for both key pairs (keylength.com)