One piece bits.
Pro: Shorter height, fits into tight spots better than two piece.
Con: If the bit gets damaged the whole thing has to be replaced.
Two piece bits.
Pro: Sometimes the bit itself can be replaced if damaged. Snap-On does this for example.
Con: Taller height, doesn't fit well in tight spots like the one piece bits. Usually more bulky than one piece bits.
I'm sure there are more pros and cons for both,These are just a few that came to mind from my own experience with both types.