Once you've weaken your enemy ship in "Assassin's Creed 4: Black Flag", you'll have the option to sink or board it.
If you decide to sink the ship, you will receive half of the resources and loot available. When faced with the option to sink or board, its best to take the time to board the ship. Once you defeat the ship you will have three options:
Lower Wanted Level: If you've got hunter ships closing in on you, you'll want to lower your wanted level. You will also gain extra crewmembers by letting them live.
Send ship to the Kenway's Fleet: Replace your weaker ships with Man 'O Wars and Brigs. They'll come in handy for the minigame you can access in the captain's quarters in your Jackdaw.
Repair The Jackdaw: If you took a lot of damage during a fight, choose this option to patch up the ship.
In order to decide which ships are best to board, use your Spyglass to spot which enemy vessel has what you need, whether it be resources like metal, cloth and wood or sugar and rum to sell for Reales.
(Note: you cannot board the four Legendary Ships)
Here are 5 tips you should know about boarding ships, in no particular order:
1.When you're facing a small ship like a Schooner, use the swivel guns and Edward Kenway's pistols to take out the crew. It will go by a lot faster and you don't even have to leave the ship.
2. Kill the captain first. He'll be marked, so you can't miss him. However, don't take too long as your crew will quickly be depleted by your enemies.
3. Scouts are annoying. Take them out after you've killed the enemy captain using the "elevator" hook. BEWARE! Scouts will be expecting you. Anticipate their moves and do not let them push you off the platforms.
4. "After seeing the sails on the ship fall--or the health fall into the red--pull up near the side of the stunned ship and hold the button shown. The region you can stop in is a large rectablge on either side of the stunned ship, highlighted in the water. If you damage the ship, with your Ram or otherwise, you risk sinking it. you can order the crew to throw hooks over and board the ship. You can now swing across using a rope." (Source: IGN)
5. Be on the lookout for powder kegs on ships. Some vessel will prompt you to shoot them as a secondary objective when boarding, others won't. If you have a lot of enemies to take out, shoot the kegs first. They'll wipe out a good chunk of your enemies.