elliptic curve encryption over RSA

The main advantage of elliptic curve encryption over RSA encryption is its computation speed. This method was first independently suggested by Neal Koblitz and Victor S. Miller.

Both encryption methods support digital signatures and are used for public key encryption and distribution. However, a stronger key per sec does not necessarily guarantee better performance, but rather the actual algorithm employed.

A comparison between traditional RSA and an elliptic curve cryptology would be helpful.
To begin with:

Advantage of RSA:

1. Well established.

Advantages of elliptic curve:

1. Shorter keys are as strong as long key for RSA (see the IEEE paper)
2. Low on CPU consumption.
3. Low on memory usage.