The short answer is yes, geothermal is slightly more efficient, and should have slightly lower bills for central Michigan.
The longer answer geothermal will not lower your bill by much, and may not lower the cost at all in your lifetime.
Two factors are at play;
1) geothermal systems cost much more to install, either because of the wells, or the trenches to install pipes. They work best when the groundwater level is close to the surface and the pipes can be set in wet soil from the service. They also have to pump water around the loops, or up and down the wells for a standing water friction loss.
2) Air cooled heat pumps used not to function well in extreme cold, but that is no longer the case. Advances in heat pump design have enabled air cooled heat pumps that function in very cold -5F to -20F.
However, for both types, you will be best served by designing a home with super insulation. E.g. 12-16" walls, with offset studs or densified fiberglass outside of the studs, triple pane windows, air heat exchanger, R60 in the attic, double door entryways, and skipping the Viking gas range with its monster exhaust fan.
Peter