The difference is in the native shape of the image.
A 4:3 projector has a shape which is 4 units wide and
3 units tall - the "unit" depending on the size of the
image. We're not talking size but aspect ratio.
A 4:3 projector has an image that is shaped like the
image on a TV. However, a 16:9 projector has an image
that is shaped more like widescreen movies, or HDTV.
You should decide what type of material you are going to
be watching the most of, and buy accordingly.
Also be aware that there are lenses like the Panamorph or
the ISCO that will effectively convert a 4:3 projector into
a 16:9 projector.
Either way - you can always display a 16:9 image on a 4:3
image - it is letterboxed - like showing widescreen movies
on a 4:3 direct view TV. There are black bars at top and
bottom - which are pixels that are off.
If you don't mind the black bars - and the fact that you
aren't using some of your projector's luminosity and
resolution - then it doesn't matter what you get.