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Use a peer-to-peer network when you want the system to keep working without trusting or depending on one central operator.

Main reasons:

- **No single point of failure**: if one server goes down, the network can still run through other peers.
- **Censorship resistance**: no central server can easily block users, delete data, or stop transactions.
- **User ownership**: participants can verify data themselves instead of trusting one company’s database.
- **Scalability through distribution**: storage, bandwidth, and validation can be shared across many machines.
- **Resilience**: harder to shut down or attack because there is no one main target.
- **Transparency**: in blockchain-style systems, peers can independently check the same ledger/state.

A central server is better when you need speed, simplicity, strict control, easy moderation, and low operational complexity.

A peer-to-peer network is better when the priority is independence, fault tolerance, decentralization, and trust minimization.