What should be broken to break a cipher with perfect forward secrecy? What should be broken to break a cipher with perfect forward secrecy as a passive observer? RSA/EC analog, (EC)DHE or both?
If the key exchange (i.e. (EC)DHE) is broken then a passive observer might be able to find out the symmetric key used for encryption which thus would allow the attacker to decrypt the traffic.

If instead only the public key or signature algorithms in the certificate are broken (that's what you probably mean with RSA/EC) then an active attacker might be able to man in the middle the connection but this ability does not help in passive attacks.