I side with 280, a well tuned bow AND ARROW the field point and BH will hit the same (assuming no wind drift etc). IF they don't there are three probably causes, all TUNE RELATED:
1) contact somewhere, most likely fletching kicking the arrow in some direction as it leaves the bow
2) Arrow tune, straightness and BH alignment come in here. spin the arrow in a spinner with the BH on it, does the tip wobble at all
3) Tune the bow to the nock is being pushed straight forward perfectly through the rest (right/left or up/down rest and /or nock point adjustments. Can also be done via cable/cam timing an yoke tuning if you have a suitable yoke)
There are more ways to get this done than you can imagine. There's no reason, given time and experience tuning, that they won't hit the same. BTW, your own form can also be an influence via hand torque etc.
