What would be the difference between buying one of these or installing a linux
distro, on your own computer?

I have noticed that the difference between using one of the companies which
builds just a white box with linux and purchasing the parts from someone like
NewEgg and building it yourself is this: you get MORE for you money when you do
it yourself and in almost every circumstance where I have been personally
involved, the quality is higher when you do it yourself. Dollar per dollar -
your best bet if dollars are tight is to purchase a Dell with Ubuntu or build
your own with known working components for Ubuntu.

I never thought about hardware, that would not work with linux, and would
normally work with winders or other os. What are the specific components that
may not work with linus distros?

I just completed an order of 100 small form factor units by Shuttle with Ubuntu
installed on them. I know they work. I put AMD on all of them. I load a flat 1gb
of ram and install 80GB drives. Ubuntu recognized everything. Of course, I'm
partial to Shuttle but others of course work.

Its not a matter of what works with this or that distro but what "just" works.
Unless its highly proprietary hardware - it will most likely work.

What one hopes to get is hardware compatibility and technical support. What one
gets in reality is anybody's guess. This is new territory for many OEMs and
consumers. Budget computers can have older technology and lower quality parts.
It is buyer beware. It may come down to whether you can count on the dealer to
give the support that you may need.

Building your own computer will require some research on your part. Find out
what equipment works well with Linux and build it into the computer. If you stay
with generic names you have a greater chance for success. The biggest problem
for Linux developers is the failure of equipment manufacturers to release
information on proprietary equipment. The biggest offenders of this are laptops,
wireless cards and some webcams. ATI is routinely uncooperative but some people
have good success with them. The key is to research.

Check out: http://www.linux-drivers.org/