It's both at once. (Though, as I said, you don't throw out extensionality. Actually, that raises an interesting question - could you discard extensionality as an axiom, and just derive it from AFA? I hadn't considered that possibility. Edit: You probably could, there's no obvious reason why you couldn't, but I honestly don't feel like checking the details...)

If you just throw out foundation without putting in anything to replace it, you have the possibility of ill-founded sets, but no way to actually construct any. But the thing is, if all you do is say "Non-well-founded sets exist!" without giving any way to actually work with them, then, well, that's not very helpful either. Hence any antifoundational replacement for foundation is going to have to strengthen extensionality if you want the result to be something you want to work with at all.