I don't find the exploration that meaningful. You have have to wonder around and find the battles. There is nothing you can get while wondering around to make the battles easier. It doesn't matter if I find the battles quickly or not.
The graphics from the battle mode seem brighter than the exploration mode. Having a 3D model of the yokai in the world would have made the two modes feel more connected.
I like the background sounds. It works well with the visuals.