Sounds to me like your rest needs to be tuned. Here is the link for the Easton Archery tuning guide. Go to the broadhead tuning section and follow it methodically. It'll work I promise, unless you have bigger issues with the bow which it doesn't sound like you have. After you tune your rest properly both field points and BH's will hit the same place.

http://www.eastonarchery.com/downloads.asp

Your broadheads magnify the imperfections of an arrows flight.

Goodluck, this should get you fixed up.