Elliptic curve systems are way slower than AES (or DES).
Also, the two are very different animals. AES and DES are symmetric ciphers, which means that the sender and receiver each need the same, secret key.
On the other hand, elliptic curve systems (like RSA) are asymmetric (or public key) ciphers, which means that only the receiver's (private) key needs to be kept secret. The sender's key can be made public, hence the name ;-). The big disadvantage of public key ciphers are their relative slowness.