They're not the same thing. They have very different implications.
You can imagine Force and thus Momentum as the "push" that will happen to the target, while Kinetic energy is the damage it causes. E(k) is equal the Work the object will perform, let it be penetration, fracture, etc.
As soon as the object hits the target, the E(k) applies (i.e. the damage). The object will transfer the E(k) over time (very short), and as it creates damage (penetrattion) its E(k) is decreasing. The penetration is opposed by friction, which pushes the target backwards with the same Force as it's stopping the bullet.
Simple example: A football and a bullet have the same Momentum, but the bullet has much higher Kinetic Energy. The push (p) is the same, but the ball doesn't have enough E(k) to cause any damage so it just pushes the target. The bullet, however, will first penetrate it "spending" it's E(k) against the toughness, hardness and other factors, and as it's stopping within the target the friction pushes the target backwards resulting in the same push as the one of the ball (unless it pierces though it, in which case just a fraction of the momentum gets transferred)
In short: Energy causes damage. Force and Momentum cause movement.