I'll add my 2 cents & a picture onto what Bbowsher said. First....in addition to the AOD being internally the same across all, I believe it is correct that all of them use the same case, expect for the tail housing and output shaft? With that being the case, they are all 1.5" longer than a Bronco stock drivetrain. That is info to correct what AA has in their tech article for using their adapter in an EB.
I look at it this way in choosing which AOD to use. Pretty much any AOD you find out there on the used market should probably be rebuilt. So.....there really is no reason to go on the hunt for the much less common 4wd version since it has to be opened up for rebuild. To use the AA adapter kit, you have to totally disassemble the trans to install the AA supplied output shaft.
You're either going to disassemble the 4wd or 2wd version to use the AA adapter kit, which includes; aluminum adapter housing, AA specific trans output shaft, AA specific spud input for D20, & various hardware, gaskets, etc.
The ONE main reason other people look harder for the 4wd version is that a full size NP205 transfer case will fit in an EB and will bolt right up to a 4wd AOD w/ no additional adapter. If you want to run a 205, then you are better to find the 4wd AOD. If you want to continue running the stock EB Dana 20 TC, then it really doesn't matter which AOD you start with.
Let me add a sidebar here......you can run the D20 with the ZF adapter on a 4wd AOD also. But, you're still buying an adapter then. What is the price difference between the ZF adapter & the AA adapter? Probably not much. What is the cost difference between the widely available 2wd AOD & the less common 4WD AOD? Enough to probably offset the adapter cost savings?!?!?!? Dunno for sure....
I've attached a picture of a 4wd AOD I used to own. You can clearly see what the Ford factory adapter(for transfer case) looks like in the pic. Everything, case length & internal wise is the same forward of the tail housing. I keep mentioning case length because in the other thread that this sprung from, (having to do with twin sticks), there is some confusion about AOD length which will have an effect on what twin stick will mount to the AA alum. adapter as JBFab intended.
There is one additional difference between AOD 2wd & 4wd. The 4wd has a factory "deep" pan. It's not deep all the way across the pan. It has a deep hump in the middle where the filter pick up snout drops into. That hump makes balancing the AOD on a trans jack during installation a real PITA! Ask me how I know.....not running that pan anymore, now running an alum. deep pan.