One Piece Bats: Typically stiffer and more balanced. The one piece design does not allow for more vibration control, so they will often have a lot of vibration on miss-hit balls.
Two Piece Bats: Tend to have more flex and have less vibration.
Generally speaking, contact hitters benefit from one piece bats for the better balance, and power hitters benefit more from the two piece bats for the added flex. The choice between the two is based on your personal preference and hitting style.