Yes, it differs. Prepotency comes into play with height, so the foal may take after the height of the dam or the sire, although most breeders like myself, feel the mare has more influence.
The main factor actually is not the sire and dam but their lines. If both are true to their breeding, you can use them as a guideline, but if either is an anomaly, they themselves may not count at all. I had a little 14.1 Appy mare that was an anomaly - her lines were all in the 15 - 16 hand range. All of her production grew to 15.2 or 15.3, regardless of the size of the stallion.
Sorry if I'm bouncing around a bit, but the bottom line is it is hard to tell without knowing more information. Without more information, my bet would be the foal will end up the same size as the dam, as that is where the best odds are...
It is really hard to tell what the height of the foal will be as you have to take in account parents height, grandparents height etc..(as Faceman explained) For example my filly was born to a mare that is 14hh, the sire is 14.1 1/2hh my filly is 3 in November and is currently standing at 14.2hh (bigger than both parents and still growing). The sires dam is 15hh and his sire is 15.1hh and his grand dam was 14.2hh (this is where the sire got his height). I hope this helps..