If your SSL handshaking is a performance-limiting step, you're doing something wrong. Yes, ECC can be faster than RSA... but it really doesn't matter for SSL.
The problem with ECC is (has been, rather) that it's covered by patents, and OpenSSL didn't have ECC APIs until very recently. I believe the implementation in the latest versions of OpenSSL are based on the work of the same authors. Unfortunately, with so much deployed code using RSA-based handshakes, it seems tough for ECC to gain traction all that soon.