See
http://www.scramdisk.clara.net/pgpfaq.html
At high numbers of equal bits DH is a little stronger than RSA.
As for key size, 512-bit RSA has been broken, but only 283-bit DH has been broken (or so the NSA says). Either way, they are nowhere near 1024-bits. The DH key max of 8192 is overkill, let alone the 16,384-bit max for RSA keys.
Either way, once quantum cryptography becomes more advanced all current encryptions will become useless. Not only will they be decrypted easily, but quantum cryptography should be undecipherable. These technologies are currently available, but semi-primitive and expensive. Standing rumor is that there is a fiber-optic cable running from the Pentagon to the White House carrying qubits
.