Alright so I’m not an expert so I might not be explaining it correctly.
Federated Network: Multiple instances sharing content, such as Lemmy
Peer to Peer Network: There is no “instances”, just peers. Many peers sharing content. Every user is a peer. There is no server costs, because every device connected to the network is acting like a mini-server. It will cost your device some storage space and network bandwith depending on the how the software is designed.
Or do you think Centralized servers are still gonna dominate the future?
P2P social networks have a moderation problem. Individual users are all their own moderators, which works like the “block” feature on Lemmy and KBin. However, this can get super exhausting so fast. There’s only so much fascist, homophobic, or transphobic bullshit a person can tolerate in an online interaction before they just give up and leave the network because it feels like there’s nothing worthwhile there.
There may be a solution to this problem someday, but for now, you have a choice for P2P networks. You can give up on user discovery entirely, as in Secure Scuttlebutt, where your network grows as you get invited to follow people or invite people to follow you. Alternatively, you can give up on moderation entirely, as with Nostr. I think either are fatally flawed presently, making federated services the best choice for having good control over your social networking experience without having to do every single part of it yourself.