Quoting my google research:
Basically, dedicated servers are stand alone units which only exist to run a game server from, whereas P2P (Peer to Peer) means that one of the people playing the game also acts as the host, and the other players connect to that player's machine.
For that reason, dedicated servers are better because all of their power is put into running the server, whereas a P2P host's computer is running the game they're playing, running the server they're hosting and doing whatever else that player may have running.