If you are just after the appearance of the homes shown in your pictures, I don't think that there would be much difference in the cost of post frame versus conventional construction.
You will save money by going up and/or down rather than going out. I don't really know whether basement space would be cheaper than second story space or not. I would think that it would depend on the lay of your land and your design considerations. Your pictures show dormers on the second floor. Those add complexity and cost to the structure. If you have bedrooms in the basement, you are going to have to provide a means for escape in case of a fire. This may be fairly cheap and easy to design if your lot is on a slope and you can have a walkout basement. It may be somewhat more expensive if your land is flat and you need to put in egress window wells in multiple locations.
Having a smaller footprint house with both a basement and second floor will can make the cost and efficiency of plumbing and HVAC systems much better. Our present home in the city has a tankless water heater in the garage---which is on the far end of the home from the master bathroom. To get a warm shower in the morning we need to let the hot water run about five minutes before we step into the shower. If the house is built on a slab, the heating and cooling ducts will likely be located in unconditioned space in the attic. Having long HVAC runs in unconditioned space is not efficient.
It's hard to talk about costs per square foot without some clarification. In our area, real estate agents quote a price per square foot by dividing the asking price of a house (including lot, utilities, garage, driveway, sidewalks, etc.) by the square footage of living area. Do your estimates include the cost of your lot, site preparation, concrete flatwork, utilities, permits, porches, garages, etc.?