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You don't have to answer if you don't know the answer.
Ok, you DID realize that WW is a moderator? The site has a policy not to do peoples homework for them. You should take that to heart else you will not find this a very friendly forum.
Now on to your question:
Well I was a big fan of z-buffering -- it is a fairly strait forward way of dealing with the problem of rendering a scene. It DOES tend to lead to poor edge definition (z-fighting). You have to remember that it is actually a false 3D... it is a set of planes really.
Back Face removal on the other hand is more 3D friendly. The biggest problem is that it only works with convex polygons (well it can do some concave polygons just not all). For this reason you need to convert all of your shapes to collections of convex polygons.
You can read up on these techniques on
sigraph.org (great place for info on computer graphics)
As for why you choose one over the other depends on what you are doing.