Neither one is secure if the private key is leaked; if the connection data is kept by and adversary then the adversary could decrypt the connection data if the private key of either DH or RSA key pair is lost.
The idea of ephemeral Diffie Hellman is that you create two new key pairs for each connection. Then you can throw away the key pair(s) after the connection has been set up and authenticated. Even if the private key is factored or otherwise retrieved then you could only attack a single connection. If the server is found by anybody then the private key would already have been destroyed, so this makes it impossible to decrypt the data when the server is found. This is what forward secrecy offers you.
RSA is not very useful when it comes to generating ephemeral key pairs. RSA key pair generation is one of the slowest algorithms that exist, and the time it takes to find two or more primes is indeterministic as well. In principle you could generate a new key pair at one side and use it to agree on a master key, just like with ephemeral Diffie-Hellman.