Why does Bitcoin support both compressed and uncompressed keys/addresses?
The reason they exist both, is because Satoshi didn't know about compressed public keys, and it was only recently discovered that they would be possible to use without compatibility problems (support only exists as of version 0.6 of the reference client).

The advantage is clear: their public keys are smaller, resulting in smaller transactions on the network, saving block chain size for everyone.

Update: inside SegWit spends, only compressed keys can be used.