What is the difference between all the AIWA Compo Boxes?

With that Yamaha you don't have to use the Basf tower because it's a combination of a cd/tuner/amplifier.
A stand-alone cd player that also plays MP3 is not very common in a small footprint, an example is the Denon @Mister X mentioned (BTW, I'm not sure it plays MP3, the manual does not say it does, and I don't like the fact that it's a 3-disc changer. Those mechanics always go wrong).
Denon also has the DCD-F107 but that one is a bit wider than the Basf system.
Teac has the PD-H380 which is 215mm wide, that matches the Basf system pretty nice, and the PD-H01 or the PD-301-X that even has a digital tuner built-in.

 

If you look for a cd player sized 210 - 280 wide, there is not an abundance of players to choose from.
The Basf=Aiwa set is 210mm wide so you have limited choice. And you want to have a bit of similar looks.

It quickly comes down to something from mini systems made by Yamaha, Kenwood, Onkyo, Denon and Sony.
The Teac I mentioned is also part of a system stack but not very easy to find, at least in this part of the world.