Is it more profitable to destroy ships for their loot or to board them?

Destroying ships yields only half of their cargo. So, it's generally better to board them. If a ship has gold, sinking it will still give you all the gold.

And, as you suspect, later on you will be able to capture ships and send them on missions to earn credits.

Destroying ships normally gives you half of each item on board that ship, so if a ship had 100 sugar and 50 rum, you would only get 50 sugar and 25 rum.

Legendary ships are the only exception to this, because they cannot be boarded. You will always get the full 20,000 gold.

Boarding a ship, in addition to the full cargo, can be

• Used to repair the ship, refilling one completely destroyed health bar (it will also refill a partially damaged health bar in addition)
• Used to remove notoriety, while also giving more crew
• Sent to your fleet. Accessing the fleet requires internet connection