As you can read above, split sole has soles on the ball of your foot and heel, but nothing on your arch. They are good for pointing your toes and tap dancing on your toes. Full sole tap shoes have one long sole that runs from your toes to your heel. They're good for doing toestands and stomps.
Which one is better? That depends on the type of tap dancing your doing. If you're doing Classical, Broadway-type tap dancing (think 42 street) split-sole works best in my opinion. If your doing rhythimc tap, which concentrates on putting sounds together in long combinations (think Bonjanles) full sole works best for me.
In reality, however, both are very usuable, and if you've already bought a pair, i wouldn't worry about running out and fixing it!