Q:

Making Clients choose preferred SSL/TLS Certificate

Let's assume we have 2 CAs "ACA" using RSA and "BCA" ECC, both issuing TLS certificates for the server. ACA is trusted by most clients while BCA is only trusted by only a few.
While ACA is trusted, RSA always takes more time. So we'd want the cert signed by BCA to be preferred by all clients that trust BCA while the others would fall back to the ACA one.
As I know, configuring multiple certificates for a domain is possible. At least on nginx, but the client always uses the certificate I have put a as the second certificate entry in the snginx.conf configuration file of nginx.
So is it possible that the server handles delivering the EC certificate if possible, but the RSA one if the client does not trust the certificate?

A:

The client does not provide any information which CA it trusts. This means that the server can not decide which certificate to serve based on the clients trust settings. The only information the server has to decide which of these certificates to use is to look at the ciphers offered by the client, i.e. use the ECC certificate if the client supports ECDSA ciphers and use the RSA certificate otherwise. 

