Let me explain it in a clearer way
Public IP will allow faster torrent speed because it enables you to
open ports for direct peer-to-peer connections.
- P2P users with public IP can connect to both private and public IP peers.
- P2P users with private IPs cannot connect to other private IP peers, because neither side can accept incoming connections.
However, most of the time, the difference is minimal as usually high quality P2P peers have a public IP.
Public IP also allow you to host your own server, NAS and etc. That's because public IP can have a direct public facing open port to allow incoming connection.
Apart from P2P, most modern apps and pretty much every online game do not care about private IP these days. A lot of ISPs in other countries do not even offer public IP anymore.
In the case of TM, I don't see a difference in routing or network policy between public or private IP AS LONG AS they are within the same IP range.