The English and Japanese versions are nearly the same. There are only a few minor differences, other than text speed.
In Dungeon 2, the miniboss can be damaged before he actually appears in the Japanese version. This saves time over English because you do not need to wait for his pattern to cycle to be able to hit him.
In Dungeon 4, the switch for the first minecart section is in a slightly different position. This has no effect on the run.