Is there any advantage to finishing battles quickly?
Like Frank said, the number of turns it takes you to complete a battle doesn't affect anything. It's just something to grade yourself on. However, the faster you complete a battle, the less enemies appear. If you take more turns, more enemies show up and you have more of a chance of losing the battle. Just take as much time as you need. If you take longer to complete a battle you may be able to obtain more items though.