PTP networks are just that- there is no regulating server to control traffic to, so you might experience some network congestion depending on the total number of inbound and outbound connections you have in one instant.Think of it as flying in an airplane - where you have radar and know where everyone is, but you aren't getting directions from the air traffic controller, you're just cruising around based upon what everyone else is doing. PTP networks are usually safer because there is no server in the middle tracking you - in the example of a torrent tracker all the tracker does it point the PTP clients towards the right address to retrieve data. The tracker doesn't care who you are or what you did 30 seconds ago, it only cares about NOW, when your torrent manager is off, you're not being observed by a server for data availability. There is still some risk but it is minimal unless you're sharing repositories of thousands of movies or something else you can get prosecuted for.
Client/Server networks are wonderful and are very powerful and fast when organized and built correctly. Traffic congestion is usually minimized because the flow is to and from one main computer in a star format instead of a web format. One single inbound and outbound connection is easier for any machine and network to handle, so if you can make use of a client/server setup, definitely go for it. Traffic flow is optimized by the server and not the network infrastructure, so there is less network congestion and speeds are typically a lot better. In a client/server situation, you can also employ rules that you would not be able to otherwise with a PTP. Quality of service, packet filtering, account control, bandwidth throttling, and permissions/rights.
PTP
Pros: Highly extensible, unregulated, open, better privacy, user has total control over connection. Custom software or protocols can be used
Cons: Causes more Congestion, harder work for infrastructure gear (no central server) and clients, generally not as fast as a client/server setup.
ClientSide/ServerSide
Pros: Fast, Organized, network owner has total control over permissions, content, speeds, etc. causes less congestion, less load on network infrastructure, traffic flow is optimized and routed efficiently, custom software or protocols can be used
Cons: End Users have little to no control over their connection, all actions are trackable and logable, connection governing rules can be set up, users can be banned, blocked, or throttled down,