If you have to punch upwards towards a taller opponent's head, you don't punch quite as hard as if you were punching straight. That's because you can't put the full force of your body behind the punch. You can still generate force with your legs though.
A taller opponent can more easily kick you in the face without needing great flexibility.
Longer arms and legs mean that your hooks and hooking kicks have a LOT more impact. It's science.
being taller means that your opponent will have a hard time getting his leg above yours. You'll see especially in Taekwondo that kicks are blocked simply by lifting up your knee. It's very frustrating trying to kick someone in the face when they can lift their knee up to your chin.
Some disadvantages to being taller than your opponent:
given the same weight class, the shorter fighter will be stronger and therefore his punches will be harder given the same technique.
the shorter the arm or leg, the quicker the strike.
if you're much taller, it will be difficult to "work the body" of your opponent.