- What are the similarities / differences between them?
- Which use cases are best for each network
- Are there more than these listed above?
If you need support on both geth and parity go wtih Ropsten. Otherwise choose Kovan, Sokol or Rinkeby as they are more stable.
Detailed version below:
geth --networkid 3
parity --chain ropsten
parity --chain kovan
geth --networkid 4
There are other networks as well, as described in this SO answer, copied here with their network id numbers:
0: Olympic, Ethereum public pre-release testnet
1: Frontier, Homestead, Metropolis, the Ethereum public main network
1: Classic, the (un)forked public Ethereum Classic main network, chain ID
1: Expanse, an alternative Ethereum implementation, chain ID
2: Morden, the public Ethereum testnet, now Ethereum Classic testnet
3: Ropsten, the public cross-client Ethereum testnet
4: Rinkeby, the public Geth Ethereum testnet
42: Kovan, the public Parity Ethereum testnet
77: Sokol, the public POA testnet
99: POA, the public Proof of Authority Ethereum network
7762959: Musicoin, the music blockchain