Privateers have to be hard-built/purchased in full, unlike Naus which can come from upgrading your old triremes. They're definitely fast and very good for exploring, plus it can get your Privateers set some flanking bonuses faster than other Privateers. As someone pointed out, Naus can eventually be upgraded into Ironclads which are definitely stronger than Privateers, which don't get an upgrade until Destroyers come in.
For naval battles in seas where my Frigates aren't around, I would allow my Naus weaken my opponent first before having the Privateer go for the kill and, hopefully, steal the ship. After which, I would let my Naus go to neutral territory to sell their exotic goods and get their quick heals.