Elliptic Curve SSL performance: ECDHE and/or ECDSA?
It is hard to give a precise percentage as you expect because performances depend on the hardware platform. But let's get into the subject.

The only difference between TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA384 and TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA384 is the signature algorithm.

Whatever, one will have to generate an ECC key pair on the fly in order to perform an ECDHE. Then, this key pair will be signed using the certificate private key. If the certificate contains a RSA public key, then the generated ECC public key will be signed using RSA. Otherwise (i.e. if it contains an ECDSA public key) it will be signed using ECDSA. Also note that one will have to verify the peer signature on top of generating his own.

So your question is equivalent to comparing RSA to ECDSA, I suggest you to take a look at How do RSA and ECDSA differ in signing performance? and Signatures: RSA compared to ECDSA.