Pump is going to be cheaper that 100% electric way down into the single digits. Different answer if your aux is gas furnace. Comfort, that is, temp of air from the vents might lead to different decision, depends if that is a concern to you.
As for me, I let the pump be the primary heat source all the time and the tstat will call for electric heat as supplemental in the background when the pump alone can't keep up.
Only time I shut her down is a bad ice storm where it can't defrost properly.