The battles are similar, but there are quite a bit of differences. There's no longer any wait times for spells or other various techniques. It takes a bit of strategy away, but not it's not too bad. Also, they have a new Judge system in this one. You get set laws in the beginning of each battle which you must follow. That wasn't in the original.
You also gain abilities in a completely different way. Before, you just had to level up your classes. Now, you have to master skills by equipping and using weapons that have the skills. Sort of like what you had to do in Final Fantasy IX.