Some major and minor changes.
Getting right to the meat of the game, Sora no Kiseki FC Evolution is a remaster of the original PSP and Windows game. Of the things remastered, the primary thing is texture resolution, lighting, fully voiced dialogue, and new portrait art for all of the characters.
The textures look amazing, along with the new lighting style. This is something I think everyone can get behind, but I'm sure it will put some people off. Colors are more distinct and crisp. Playing the Vita and PSP version side-by-side, one of the biggest differences is the lighting. Almost all of the textures are upgraded, but the lighting will really catch your eye. The game is a lot brighter than the original. I don't know if this is because of the PS Vita's screen or not, but I tend to think it's a much better looking game because of it.
They've added more combat turn bonuses. Zero Arts and Zero Crafts allows you to use a craft or art at a cost of 0 EP or CP respectively. They also added a Rush bonus that makes your first attack give a delay of 0, which means you can get a free turn right after.
Another addition to combat they've added is the ability to hit enemies before engaging them. Like a lot of games where you have to actually run into enemies to start a random battle, you can now press O to attack them. Hitting from the front immobilizes them, and hitting them from the back stuns them, granting bonus XP at the end of the fight.
My only gripe would be that I personally might hate Estelle's voice. Not because it's a bad voice actor, but because I hate the cutesy obnoxious female Japanese anime character voice acting style.
Something more hardcore players might dislike is the changes to combat, which I think will make the game overall a lot easier. I'm not far into it, but leveling will be faster cause of the 2x XP Bonus from stunned back attacks (which you can choose not to use), fights will be easier due to Zero Arts and Zero Crafts (free arts and free crafts are crazy), and Rush giving you free basic attacks.