Should new applications still use RSA? Is it worth going down the ECDH route for protocols?
Accordingly to a previous thread Why is elliptic curve cryptography not widely used, compared to RSA?, RSA is still widely used compared to ECC because:


RSA is well established
Its public key operations (e.g. signature verification, as opposed to signature generation) are faster than ECC
(most importantly) The RSA patents have expired, while a small company called Certicom holds a number of EC-related patents. 


However, according to the NSA website, Elliptic Curve Cryptography provides greater security and more efficient performance than the first generation public key techniques (RSA and Diffie-Hellman) now in use. Thus, they decided to move to elliptic curve based public key cryptography for protecting both classified and unclassified National Security information.