If broadheads and field points don't strike at the some point of aim, there is a tuning issue some where in the set up. Might simply be that the broadheads aren't spinning true. Could be too weak of spine, or too stiff, on the arrows. Could be the shooter putting torque on the bow when gripping to shoot. Could be center shot off on the rest.
Several reason why a fixed blade broadhead won't impact where a field point does.
But as was mentioned above, the weight of the broadhead should be determined by figuring out 10%-12% forward weight of the arrow. In general, heavier arrows need a heavier broadhead, and visa-versa for lighter arrows.
Houndmen28, for rabbit and squirrel, you should look into the small game heads such as the judo points, or the small game heads made by Montec. Both of them will kill small game but also will often make finding your arrows easier because those heads tend to snag on weeds, dirt, limbs etc. and keeps the arrows from burrowing under stuff and dissappearing.
For the record, I use 100 gr. Magnus Snuffer SS for all my big game. Use the Magnus Bullheads for turkey.