Summary: Which is better, a crawl space foundation or a concrete slab foundation, depends on several factors besides cost.
Cost of 2800sq feet crawl space vs. concrete slab, which is best overall beyond cost?
Concrete slab foundations built on grade (level land) are easy to excavate and are installed quickly, speeding up the construction project. After all, when the slab is finished, you already have the 1st floor done and you are ready for wall framing in a day or so.
If the land is not level or the water tables are high, a raised slab foundation can be utilized.
But concrete slab foundations have their drawbacks. Slab foundations are considered by many as "cheap" and this can and will affect the homes' market (resale) value.
Concrete slab foundations are also hard on the human body, walking or standing. They are also cold.
Unless you install a radiant heat system in the concrete slab, concrete slab foundations can tend to make the house uncomfortable in colder climates.
With concrete slab foundations HVAC installation is more difficult too. In days gone by, HVAC contractors would install heat and air duct work in the slab. This eventually proved to be disastrous as the duct work often filled with ground water resulting in mold, mildew, HVAC failure and very expensive repair work.
So now, when slabs are used, HVAC duct work is installed in the ceilings of the 1st floor resulting in a little more expense and a little less efficiency in heating. However, duct work in the ceiling does improve air conditioning efficiency.
Crawl spaces aren't that much more expensive than a slab and you gain the ability to install plumbing, wiring, and duct work more easily and therefore less expensively.
Crawl spaces are warmer in the winter and easier on the human body walking on softer floors above.
However, crawl spaces have their problems too.
If moisture in the crawl space is not controlled it can build up and cause wet wood, rot, and mold. Crawl spaces are also prone to insect infestation.
Crawl spaces should also be insulated!
I have extensive information on all this on byoh.com so you may want to spend some time reading it.
I feel that the foundation, while not a glamorous part of the house, is the most important part of the house. I would rather economize elsewhere.
Foundation problems are the most frequent questions I get.
Roofs, windows, doors, etc. can always be repaired or even replaced if necessary, but the foundation is permanent. Foundation problems are far easier to prevent than repair.
If you can afford to spend a little more money, and if the local water tables permit excavation for a full basement, that is the best way to go and it is, in my opinion, money well spent. I learned this the hard way.
You also gain future expandable space. Good luck, Carl Heldmann