The two story house would probably be lower cost to build. I’ll use a 2,000 sq ft house to illustrate. With a ranch, you will need a 2,000 sq ft basement (materials plus excavation) plus a roof over 2,000 sq ft of ceiling. With a two-story house, you’ll need 1,000 sq ft of basement (materials plus excavation) plus a roof over 1,000 sq ft of ceiling.

A two-story house *may* also cost less to heat. In general, a compact house will be more energy efficient than a sprawling house. If you want to save on energy costs, stay away from cantelever floors or unusual bump-outs and keep the design compact. And spend extra on insulation and air sealing that is more than code minimum. It’s much easier and cheaper to do while the house is being constructed than to try to retrofit later.

Basement bedrooms are for guests you do not want to stay long.

Mark, you have tunnel vision and are regionally biased by not studiing or being aware of patterns nationwide (this board is not only nationwide but international). In my area, in the Rockies, walkout BASEMENTs (referred to by that term by local architects, realtors, and governmental authorities)) are often preferred by guests. In fact, I let the last THREE sets of guests choose between the upstairs guest room and the basement guestroom (which has a slider to the lower patio and hot tub) and all chose the basement even though all other amenities were equal, except that most basements, like ours, has an adjacent secondary living area not found on the second floor.. In fact, 1/2 duplex townhome 4 houses down from us just sold for 4.125 million with 5 bedrooms, two of which are in the BASEMENT. I truly doubt that their basement dwellers feel that they are second rate guests.

In response to the OP’s question, it depends on many factors and probably varies regionally. Here you have to dig deep anyway so the added cost for a basement is relativelt inexpensive. Finish is finish whether above grade or below.

"Basement bedrooms" refer to rooms used for sleeping in the foundation space below the first floor of a house and has the required egress window. Rarely do I see a bedroom created below the first floor that does not have sufficient windows and situated where one would not know they are below grade level. The more windows in a bedroom the more natural light and natural ventilation can be achieved and the less it feels like a room in a basement. When guest want to stay in a basement bedroom, they either do not like their host, or somebody did something right.

In a couple of weeks, my wife and I will be staying in our brother-in-law's basement guest room. They may not be wanting for us to stay long; and I designed it.

The OP did not mention placing bedrooms in the basement. He asked about costs of a 1-story house with a basement vs a 2-story house with a basement. I stand by my original comment that a 2,000 sq ft basement will cost more to construct than a 1,000 sq ft basement. Of course, once the larger basement is constructed, the owner will have more living space in the 2,000 sq ft finished basement than in the 1,000 sq ft finished basement.

To further your unrelated discussion, here where I live in Northern NJ, we have a lot of steep lots that lend themselves to walk-out basements. One of my favorite houses is on a steep lakefront lot. It’s a ranch and the master bedroom suite is located on the main level along with the open floor plan living room/dining room/kitchen, plus a powder room. The walk-out basement features two additonal bedrooms a full bath and another living room. Its a 3 bedroom house and 100% of the living space has windows with specatacular views overlooking the lake! The main level features a large deck across the entire width of the house overlooking the lake. Below the deck is a patio that also overlooks the lake and is accessible from the second living room in the walk-out basement. I love it! The basement absolutely DOES NOT feel like a basement! The space not overlooking the lake is used for other non-living space functions. On the main level there is an attached garage on the street side. In the basement, there are mechanical rooms and storage rooms on the street side which is underground. 100% of the living space has lake views, INCLUDING the rooms in the basement.

Depends on where you are building, local soils conditions, local labor and materials costs, size of home, etc.

Likely a walkout is more cost effective IF you follow the terrain without too much of a "dig in" that requires tall interior foundation walls, etc.

Usually local builders can give you the best info.

So in my area let's say slightly larger footprint 3000 sq vs 2000 sq ft basement will cost may be extra $20k and may be another $10k for a shingled roof and trusses [not really that much]. So think of that as 30k of 500k construction + 6%. But one story could also be easier to build: framing, sheathing, bringing drywall, plumbing, installing siding, painting and avoid the crane, lifts charges. It will also command the higher price in todays market.

We have a one story with a walkout. We discussed adding a loft while we were building. The additional floor plus hvac plumbing and finishes would have been another 100k. But that would have been adding 1000 finished square footage up. Our basement concrete was 40k for our 2000 sq ft one story. Why not ask a local builder. They probably have recent builds that could compare a two story to a one story.