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I know that DH can be used for perfect forward secrecy but for the sake of this example, let's say that RSA and Diffie-Hellman are both used to establish a symmetric key that will be used for future encryptions.
Which one is more secure or more vulnerable if the secret key was ever leaked?
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.
Diffie-Hellman is better, but only when you use ephemeral DH.
I think, your question makes no sense. More then asymetric cypher I would call DH a secret exchange protocol. It's very simple. In modular arithmetic (mod p) both sites exchange A^x and A^y mod p. Where x and y are kept in secret. They are both able to calculate A^xy mod p and use it as a secret. With eliptic curves, it's same, just multiply operation is defined differently. Where is the public/secret key?
