With RSA key exchange, if somebody ever gets your RSA private key, they can decrypt all past and future traffic that was protected with that key. With ephemeral Diffie-Hellman key exchange, even with the RSA private key, they cannot decrypt that past and future traffic, because each session has its own unique encryption keys that are independent of the RSA keys. They can only impersonate you to intercept future traffic, and only if they set up a MITM attack, but that kind of active attack is MUCH harder to execute (especially undetected) than the passive attacks that RSA key exchange allows. And, again, it doesn't allow them to decrypt past traffic at all.
This advantage of ephemeral key exchange is called "perfect forward secrecy."
For example, let's say you are a dictator and you want to decrypt some encrypted GMail sessions you suspect were done by dissidents in your country last month. If those sessions were done with RSA key exchange, you could steal the RSA private key from Google today (admittedly a very difficult task) and then decrypt those past sessions. If (EC)DHE key exchange was used, it would be practically impossible (no exaggeration) to ever decrypt them.
With RSA key exchange, if somebody ever gets your RSA private key, they can decrypt all past and future traffic that was protected with that key. With ephemeral Diffie-Hellman key exchange, even with the RSA private key, they cannot decrypt that past and future traffic, because each session has its own unique encryption keys that are independent of the RSA keys. They can only impersonate you to intercept future traffic, and only if they set up a MITM attack, but that kind of active attack is MUCH harder to execute (especially undetected) than the passive attacks that RSA key exchange allows. And, again, it doesn't allow them to decrypt past traffic at all.
This advantage of ephemeral key exchange is called "perfect forward secrecy."
For example, let's say you are a dictator and you want to decrypt some encrypted GMail sessions you suspect were done by dissidents in your country last month. If those sessions were done with RSA key exchange, you could steal the RSA private key from Google today (admittedly a very difficult task) and then decrypt those past sessions. If (EC)DHE key exchange was used, it would be practically impossible (no exaggeration) to ever decrypt them.