I'm not sure if ECDSA is somehow cryptographically better than RSA. Let me know your views.
For bitcoin I never asked such question. Bitcoin expects signature are ECDSA, you don't have any choice.
Whether RSA or ECDSA is better is a cryptography problem, such question is more suited for expert mathematician. (which I am not)
Economically speaking, I would say actors have more incentives to break RSA than ECDSA, because RSA is more used. But such claim comes only from personal observation and not backed by fact.
The weakness of ECDSA lies in the basic signature creation, the non-deterministic method.
The problem is that if people are using a RNG with poor entropy for the signature creation, the signature of any data will compromise their private key.
The point of
http://tools.ietf.org/html/rfc6979 is too find a way to get deterministic signature that does not depends on an underlying, possibly rooted, RNG.
