"Pirates of the Burning Sea" is similar to that I think, also being an MMORPG. I've played it but I haven't tried Pirates of the Caribbean Online so I can't really compare. Basically player is the captain of their own ship and it has this whole naval combat system with boarding gameplay and everything.
"Uncharted Waters" by KOEI (they do make more than Dynasty Warriors) is also in a similar vein. There's on foot combat when exploring but I don't think there's boarding gameplay. Like you can board, but it's just number crunching I think.
And if you're a little loose with your definition of naval combat then "Star Trek Online" which went F2P recently sort of applies. Similar concepts like maneuvering your ship to fire weapons or defend and what not exist. There's an added layer of strategy to it with the directional shields and hull with weapons that damage one or the other specifically.
And actually "Allods," despite people calling it a WoW clone, has a really interesting ship combat system. Rather than the typical raids and etc. the end game of Allods lets players purchase extremely expensive air ships, letting them explore floating island. They're really expensive so typically only guilds can afford it. In the end the ship is crewed by multiple players, with some controlling the movement, or manning cannons, navigating, etc. The idea is that you journey out into the ether and find uncharted floating islands for loot, the farther out they are the more valuable the treasure is, but the rewards aren't permanent until you make it back to port, so along the way other ships crewed by guilds of the opposite factions can attack and even board yours and steal your treasure. It's a very interesting system, on paper anyway, I've never gotten that far to experience it myself.
