The biggest difference for me is in censorship resistance.

On AP you have an account with a server and are at the mercy of the admins of that server. They can (and must) decide what gets deleted, and which other servers can peer with yours. E.g. many AP servers block Gab. The "community = server" model also let to some communities being shut down for being contraversial in some way.

With nostr your account is just a private key, meaning you are not tied to any relay, and your client even pulls from many simultaneously. This gives relays the freedom to block whatever content makes them uncomfortable without infringing on anyone's speech, since users can just pull it from somewhere else.