I admit, I'd prefer the depth of x3 in the elite universe. I loved FFE. But alas, that's a derail.
Back on (sorta) topic. Someone mentioned the Pirates of the Caribbean game. That was actually originally intended to be a Sea Dogs, sequel. So look into that series as well. It's actually a pretty good series, but the PotC game was rushed out of the door. Disney basically found a company working on a nearly complete pirate game around the same time as their movie, bought the rights to it, rebranded it and told them to have it done by the movie's release date. Thus, we ended up with a rushed out the door game that had a lot of potential but still fell short. I think the original Sea Dogs was, while slightly less advanced, significantly more polished.
The original Port Royale, and to a lesser extent Port Royale 2 are also worth a look. I've played both, and they both get mixed up in my mind a bit, except for the combat. In Port Royale 1 the combat was closer to a strategy game where it was fleet on fleet. In 2 they limited you to using one ship at a time, even if you were going up against 4 or 5 at a time. While this did simplify things a bit, it also made larger battles somewhat one sided. It was more of an economic simulator though, it allowed you to set up trade routes, hire captains, and one, or both games, I forget which, allowed you to actually found your own town, late game. Earlier than that though, you could create your own buildings in some towns if you had a good enough relationship with them, allowing you to not only trade between towns, but to produce goods as well (Or simply make warehouses so you could trade at towns without actually needing your ships there. Allowed you to better take advantage of the markets when prices were low or high.)