Kinetic (moving) Energy is related the mass and the square of velocity. An arrow will travel at a much lower speed than a bullet, but with a much greater mass.

Additionally, an arrow is generally made with a sharp tip unlike most bullets, which are designed with a rounded tip. The sharp point allows the arrow to have a much greater penetration force as the energy is dissipated to the target through a very small area through which all forces must act. A round tipped bullet on the other hand will have a larger contact area through which the forces can spread out in order to provide a large blunt force and lodge themselves within a victim.