Punch and Power bows are situational.
Punch bows are best when you:
* Have a side angle on your opponent
* Have an edge to shoot someone off of
* Are attacking someone on a pillar
In these situations, a Punch bow is usually a one-hit KO.
Alternatively, a Power bow is best when you:
* Have a tight area where someone can't run
* Have to fight someone with superior gear
* Are trying to deny someone access to an area that isn't over the void
Recently, I've been using Power bows rather than Punch bows, because if you have good aim they allow you to continuously attack someone, even when they are fleeing, and you don't have to wait until they attempt to cross a bridge.
That said, a Punch bow can be an excellent island defense weapon. I would argue, however, that the price of each should remain the same.