Despite both being advertised as privacy-focused cryptocurrencies, they are very different.

Monero uses ring signatures, RingCT, and stealth addresses to hide information on the blockchain. For every transaction, there is no way for an outside observer to determine the sending address, the amount sent, or the receiving address. Optional transparency can be provided off-chain by giving the desired person(s) the view key. Monero can be used with Tor or I2P manually, and Kovri is being worked on to provide native anonymous routing functionality.

Nav Coin uses trusted clustered servers to process transactions. When the "anonymous" option is selected, transactions are sent to these servers, which conceal the recipient address from others. It does not protect the sender, it does not hide the amount, and there is a trusted party that is omniscient in this process.

In summary, Monero protects significantly more information about all transactions (not just a select few) without using a trusted party.