Are there advantages and/or disadvantages of building on slab versus on crawl space or basement?

There are many different issues to consider when it comes to the choice of a basement, crawl space, or a slab foundation for your new home. In many parts of the country, full basements will be the norm, while others will have slab foundations and still others will have crawl spaces. This is simply a value / price perception issue since many people feel that having a full basement gives them more room even if it is used only for storage purposes. Moreover, of course, the potential is always there for someone to finish the basement and add extra living space at some time in the future.

Slab

Slabs are very popular in warm climates and also in areas with lots of rock. If there is no basement, the wiring and the plumbing will be in the walls or in the ceilings. Space will also be required for the furnace and the water heater within the house. Water pipes must be insulated especially if they are in the attic.

One major advantage of slab foundations is that there is little chance for water and outside gases to leak in providing a healthier environment. Also slabs are lower to the ground as a rule and they have fewer steps to go up which can be an advantage for older seniors or people who have difficulty in climbing stairs.

There are several potential drawbacks to slab foundations. Any cracks can cause long-term problems and are more difficult to repair. Soil movement, tree roots can lead to cracks in the slab. Slabs homes are also more prone to insect problems.
Slab foundations are made up of a concrete slab that is typically 6 to 8 inches thick. The house then sits on the slab. Gravel is laid out first to facilitate drainage from underneath. Often times piping and utility hookups are set up to run through the slab. Rebar is used in some cases for added support, and expansion joists, or grooves along the surface inserted to handle any sort of cracking that might occur during the curing process, are added to all slabs as they are finished. Slabs are used most often in areas where there is high clay content in the soil. This can cause problems with settling due to inadequate subsurface drainage.

Slabs typically are the cheapest and fastest foundations to build. There is little excavation needed to set the slab, and it is poured simultaneously with the footings. The preparation for pouring the slab should be a day or less including the dry time for the concrete. Slabs are also less expensive then the other foundations because the floor of the home will sit directly on the slab, this eliminates the need for a floor support system to be constructed.

When it comes to the ductwork installation there could be some advantages and disadvantages.
Considering that in some instances building a basement isn't a feasible option that I would recommend for installation of the underground ductwork. Relatively recently instead of spiral metal pipes some companies started to use plastic ones, which have infinitude lifetime and built-in insulation.
Other than that, personally, I consider building a house on a slab as a crime! Why that?
Because in the most cases house on a slab has heating/cooling equipment in the attic and this creates multiple problems. Read more on the "Ductwork in Attic" page.

Crawlspace

Crawl spaces need to be insulated and protected from the elements in the colder climates. Warm climates tend to have semi-open crawl spaces, which are a place for moisture, mould and rodents to collect. There are a number of health issues that can be aggravated by moisture and mold.
A crawlspace foundation is where the home is supported off of the ground level by approximately 2 feet. Stem walls extend from the footings around the perimeter of the foundation to support the home. Often times an alternative is used instead of the stem wall. This is called pier and beam. This is a system piers, which are a formation of rebar that are placed in holes and filled with concrete, that are tied into beams that will form a similar stem wall to support the home above. Crawlspaces are typically used in areas with high moisture, where excessive water can build up. Supporting the home off of the ground keeps it away from moisture that could cause damage.

Crawlspaces can be a fairly inexpensive foundation to build. There is often little excavation needed due to the home is supported off of the ground, and very little concrete is needed since it is only required in the footings and stem wall.

When it comes to the ductwork installation, building a house on a crawl space is a crime, hands down! It is even worse than ductwork installation in attic! Why that?
Because a crawl space, and especially a shallow one, is barely reachable for installation and maintenance purposes.
Installers in the crawl spaces would never able to do the job properly because of the working conditions they must work in.

Mechanical inspector who in the most cases is a retired heating contractor would never crawl in space like this unless a homeowner is a CPR certified and all the money saved on a concrete slab and walls will be wasted on higher prices of heating/plumbing/electrical installations and future repairs and maintenance.

Look at this photo on the left. There are two houses, side-by-side, built on the low ground on the lake's shore. House to the left sits on the shallow crawl space, and house to the right on the full size basement. A wise builder built house to the right, but a moron, whose main goal was to safe a few bucks built house to the lift.
Ironically that house was burned down to the ground, but they rebuilt it the way it was before!?!

New Light in Crawl Space (Building Science), PDF

Here is an example of professional crawl space furnace installation. 

Basement

A basement is a popular foundation due to the added functionality it brings to a home. The basement can be used as storage space, finished off for living areas, or both. This living space is often finished off as recreation rooms, added bedrooms and bathrooms, and depending on the slope of your lot, nice windows and doors can be placed to make a walkout or daylight basement. The basement foundation combines elements of a slab and crawlspace. The floor in a basement is basically a slab, and the floor support system is what a crawlspace uses. The days the walls of the basement are most offered poured, but the decision between poured or block walls is often determined by local building codes. You can find basements all over the country, but areas with high water tables or unsettled soil will probably restrict you from building a basement due to potential flooding or cracking in the foundation walls.

Basements are the most expensive of the three foundations to build. More labor is required to excavate the site, pouring the walls or setting the concrete blocks, and a basement is going to use more materials. A basement is also going to take more time to build. This is due to the added amount of work and the extra time needed to let all of the concrete set. An average basement will take 2-3 days to pour the concrete and up to a week to set.

Basements tend to be cooler which can be important in hot climates, they add value to the home and provide more room whether finished or not. Basements tend to be more expensive due to the footings and walls that must go below the frost line.

Drainage is very important for basements and crawl spaces – as you don’t want water in these areas. Slabs and crawl spaces are generally less expensive than full basements to build, especially in conditions were there is a great deal of rock to be removed. In some locations it is almost impossible to install a basement without the large expense of removing solid rock.

When it comes to the ductwork installation, the basement is the best place for your heating and cooling equipment. It would provide a necessary space for your almost entire ductwork system. Convenient overhead location allows easy access to all its elements, which contributes to easy installation, repairs and maintenance.

Below you can see some pictures taken from my "Ductwork Installation Guide" that show you how heating/cooling equipment, ductwork and some ductwork/venting elements should be installed.

Rules of Thumb for Duct Systems PDF

Basically, installation starts from joist's panning for cold air returns. (Chapter #34)

Next, follows furnace installation (Chapter #37)

Plenum installation (Chapter #38)

 
Install cold air return ductwork (Chapter #40)

Install supply ductwork (Chapter #41)

Install heat runs (Chapters #43, 44)

Install fresh air, combustion air and kitchen exhaust (Chapters #47, 48)

Upon completion of all ductwork installation do the venting (Chapter #49).

The next follows installation of condensate line (Chapter #50)

Install a humidifier (Chapter #51)