This is a hard one. Because If you ask me, Shika would be smart enough to never combat Haku 'normally', by pitting each other combat skills against each other. SHika would probably RUN AWAY. Thats whats he's most good at. And probably come back some other time.

But under abnormal circumstance, like Naruto stupidly enough, or Sasuke.. Stupidly enough. Haku would definitely own Shika.