It looks similar, but the cross kick is actually a straight leg method. Turn the hip to drive the thigh, and the calf pops up and hits the target in a straight line. Before reaching the straight line of the target, the calf is closed at the thigh. Whipping the leg is more like a spin kick, turning the hip to drive the thigh and calf to hit the target.
Comparatively speaking, the kick is more powerful, but the cross kick is faster.
Kicking is more powerful in actual combat.
The most commonly used cross kick in taekwondo competition is because it is faster and easier to score points, not because of its strong attack power.