From StrategyWiki, the free strategy guide and walkthrough wiki

[edit] Unlock Sword Beams

Simply retrieve the Master Sword in A Link to the Past to unlock Sword Beams in Four Swords.

[edit] Unlock the Riddle Quest

To unlock the Riddle Quest in A Link to the Past you must obtain 10 Triforce Medallions in Four Swords.

[edit] Unlock the Hurricane Blade

Complete the Riddle Quest in A Link to the Past. This move will then be available in both games.

[edit] Unlock the Palace of the Four Sword

You must beat Vaati at least once in Four Swords in order to be considered "a true hero" and be allowed into this dungeon in A Link to the Past.