A quick check on ssl labs says a site I'm familiar with sends 2717 bytes of certificate matter with an ECC entity certifcate, and 2921 bytes with an RSA entity certificate. The intermediate is the same for either chain, and it doesn't send the root.

204 bytes is not that much, and I'd have to run packet captures to check how much other data is going into a TLS handshake, but that seems like it is going to be throwing an extra packet in for some people, depending on their effective MSS. This particular certificate has 7 Subject Altnerative Names, the difference for a smaller certificate would be a larger portion of the handshake data.