Object-oriented networking

A map of handler instances is pretty much the best way to handle it. Nothing inelegant about it.

About the way to handle the packet type: for me the map is the best. However I'd use a plain array (or a vector) instead of a map. It would make access time constant if you enumerate your packet types sequentially from 0.

As to the class structure. There are libraries that already do this job: Available Game network protocol definition languages and code generation. E.g. Google's Protocol Buffer seems to be promising. It generates a storage class with getters, setters, serialization and deserialization routines for every message in the protocol description. The protocol description language looks more or less rich.