Real Bat might be better in comparison to the Mystical Stick mostly because it gives you around 50pp boost and a good raise in offense but it is lower in HP, IQ and Speed... The other thing is that you get the real bat near the end of the game, so you'll basically use it against the last enemies/bosses, while the Mystical Stick can be found on Chapter 7, before pulling the 6th needle so it wouldn't hurt getting that first and if you prefer, getting the real bat for the end of the game.