Masts: The number of masts is the same as the number of cannons, so more is better. It also determines how many hits a ship can take before becoming derelict, so it's a measure of damage resistance. More masts also makes a ship more resistant to ramming damage, and makes her more effective in boarding actions. The majority of ships in the game have 2 or 3 masts. 5 is the max for most factions; the Jade Rebellion has some 6-masted junks, and there are a few enormous limited-edition junks with ten masts.
Masts on a schooner aren't as likely to block other masts' line of fire as square-rigged masts, so schooners have a slight edge in battle for this reason. Galley masts badly block their own ship's lines of fire when shooting ahead, astern, on the starboard bow or the port quarter, while the port bow and starboard quarter's lines of fire are wide open. Masts on junks don't block lines of fire by definition.