Yes. I mean if by better you mean better ballistic performance, yes composite bows shoot faster, farther and harder because:

1. Composite bows have more reflex. That is, a longbow when unstrung is straight, a reflexed bow is bent forward in the opposite way. When a longbow is strung there's almost no tension in the string while a reflexed bow has already been bent and tensed quite a bit just to string it. In terms of shooting, this means longbows only accelerate arrows at the beginning of the shot and not so much near the end as the bow uncoils while a reflex packs a lot of energy throughout the bow.
2. Recurved limb tips improve smoothness at the end of the draw. At the end of your draw when the angle between the string and limbtip is significant, recurved tips maintain a more efficient lever point for the string keeps the rate at which the bow gains weight lower. This again means you're packing more energy just before your final draw length.
3. Horn/sinew are more flexible than longbows and means composite bows can be strained more by being pulled more. A higher draw length affects the energy storage of the bow as much as the draw weight does. While a longbow is typically shot at draw lengths of 28" (and expert archers in the past would draw to 30" next to the head), Asiatic draw lengths are typically much higher, about 32", past the head. Longbows can be made to draw longer but that requires making the limbs longer too (see next point).
4. Smaller and lighter limbs keeps the virtual mass of the bow low. When you shoot an arrow, you're accelerating the arrow's mass but the limbs have to get moving in order to pull the string which launches the arrow. This inertia of the bow is called its virtual mass. The heavier and bigger the limbs, the heavier its virtual mass, and less efficient the bow. More energy goes into getting the limbs moving and less energy goes into the arrow.

Points 1, 2, and 3 mean composite bows store more energy, point 4 means composite bows use that energy more efficiently. This is true at all load factors, composite bows will generally always out shoot a longbow (given the same draw weight), even with heavier arrows though people generally assume longbows are better at heavy arrow shooting. It's just that their low virtual mass means composite bows are exceptionally good at shooting light arrows fast and far.

What the longbow does have going for it is that they're easy to make, a good bowyer could turn one out in just a couple of hours and the only maintenance it would need for its lifetime would be some oiling to protect the wood from moisture.

Meanwhile a composite bow takes months to make, sometimes as long as a year depending on the climate because the components have to be glued and let dry completely before adjustments to tillering can be made. Even after it's finished the the bow has to be shot and heat tillered for about a year, before the bow starts to shoot consistently without the limbs warping and flipping front to back. If the climate is humid, the bow will have to be kept in a special heated box to be able to keep the sinew dry for shooting. You pay for the extra performance with a much higher initial cost and require constant caring for.

I feel this is an odd question. The two bows might be somewhat similar in effect (i.e. shooting an arrow across a distance), but have different purposes. It's like asking if a sniper rifle is a better weapon than an assault rifle. They have two different battlefield uses.