Common collector is also called an emitter follower. It has very close to unity voltage gain (.99 -> .998) and a high current gain. This allows it to be connected to a source which has a high impedance, such as a crystal gramophone pickup and a low impedance such as a long cable.
Common base connection is the opposite, it has unity current gain , low input impedance and a high output impedance and low distortion. It has a high voltage gain.
Common emitter connection is intermediate, medium input impedance (3k?) highish output impedance (10k?), large current gain and medium voltage gain.
Frank