The debate my wife and I have is should we close the doors to rooms we are not in at the moment, or keep them open to equalize the temps across all rooms?

A couple of points to consider:

1. We have a 1200 sq ft unit on one level, we face North however are pretty well insulated from direct exposure to wind/cold as our unit is is on a lower floor of a U shaped building, we actually overlook a swimming pool. In the summer we almost never run the AC as our unit is keep pretty cool, the flip side however, is that during the winter the unit will get pretty cold without running the heat.

2. Each room has it's own heating and cooling unit (electric)with thermostats, so they can be regulated independent of each other.

3. The building is about nine years old and is concrete and brick, all the floors are carpeted and we have very good insulation on the front door and patio door.

If the doors are always closed then I would think more energy is expended in getting that room that has been closed for a few hours back up to a comfortable temp.