The major changes are in the character classes and party members. Similar to FFL, starting a game of Legends II allows you to choose your main character from Humans, Monsters, Mutants and a new class: Robots. From here, you build your party of 4 from the same character classes. During gameplay special side-characters will join you in battle to help defeat certain enemies.
Play Final Fantasy Legend II for Game Boy online
The other improvement is in strategy. In FFL you gain experience points after each battle, increasing strength, etc. In FFLII, you gain different points and abilities depending on how you defeated the enemy. If you win by using a sword, your strength increases. If you use magic, your mana increases. This adds a more strategic approach to defeating enemies.