Nothing has really changed as much, updated graphics are pretty. But the leveling up system can be a drag and annoying.
The plot for Final Fantasy II begins as Firion, Maria, Guy and Leon are attacked by Palamecian soldiers and left for dead. Firion, Maria, and Guy are rescued by Princess Hilda, who has established a rebel base in the town of Altair after her kingdom of Fynn was invaded by the Emperor. You are pretty much finding and searching for ways on taking down the Emperor and pretty much trying to save the world.
Gameplay: If you've played its predecessor Final Fantasy, you can freely roam an overworld containing several towns and dungeons. While roaming around the world traveling town to town, you'll encounter random battles which can occur at any time during the overworld map or in dungeons.
Each battle you can attack, defend or use items in battle, most of the enemies can be really easy to beat which can take a few seconds to defeat and pick up its rewards like Gil and Exp; but it can be a little bit of a drag fighting the same enemies over and over. You can learn spells and magic which can be used in Battle, but you'll have to buy them in the shops in various towns and you can choose which characters you want use to learn the spells.
What you may find annoying about Final Fantasy II is that there is no levelling up system; you won't be able to level up your characters to levels like level 60 or higher. But instead you'll be able to increase your HP and MP for your characters along with strengths and abilities. Another thing you may find annoying is that you may not know where you need to go next, you may want to look for a walkthrough if you are completely helpless but you shouldn't a problem finding where you need to go next.
Graphics and Sound: The biggest thing you'll notice about the Anniversary Edition is that the graphics and visuals are pretty to look at on a PSP. It still has its 2D backgrounds and sprites, but everything is crisply detailed and beautifully drawn for its characters and CGI cutscenes at the beginning before the main menu pops up to a new game or Load game. Unlike most RPG being in 3D there is nothing else to talk about its graphics and it doesn't have any camera issues, most RPG games would take forever for levels or areas to load each time.
The PSP version of the Anniversary Editions for Final Fantasy I and II its loading times are short and quick to appear from popping up to its main menu system or go through various towns and dungeons. If you own a PSP Go it only takes 203 MB on a memory stick.
Music is well polished and modernized so if you did play Final Fantasy II in the past on the PS1, its tunes you know and loved haven't really changed as much back then. There is no voice acting but there is a lot of text-dialogue to read throughout the main story.
Overall: The Anniversary Editions do make a great touch for the PSP and a chance for players and fans to play some classic Final Fantasy games before they were made in 3D like we have today for most RPG games. Beating the main story can take you 40 hours or less pending on the number of the goodies you pick up along the way including an extra dungeon which is added in.
It would have been nice if this was released along with Final Fantasy I in one collection instead of buying them separately in stores or on the Playstation Store but it isn't worth the price paying them each.