Armory boots are 2-piece units. Toyfair Batman were the classic 1-piece units.
Also, beware that some models (DX11 possibly) were 1-piece units but made of a slightly different rubber that had a chemical reaction with the older figure's rubber when you used them together. Don't remember which combination was toxic though - hopefully someone else remembers, otherwise you should do some searching on these threads to double check.
Yes, your correct that the original DX02 and Toyfair version are 1 piece boots whereas the armory and DX12 (DX11 is the Joker) are 2 pieces, as are most newer figures. The 2 piece design gives way better ankle pivot and articulation vs the 1 piece.
Texasfinest, I doubt as this point you'll find DX02 boots, and you wouldn't want another set of the toyfair boots as they basically all cracked over time. I've posted before in this thread. I own the toyfair ex and bought the armory boots but never used them as mine is still boxed up, and although fine when I received it, just sitting in the box over time the ankles still cracked. Mine can still stand just fine, one boot still kinda snaps in, the other rests in. I bought the boots to be safe as down the road if I do display him or sell him, I have replacement boots.
As far as chemical reaction, I had bought 2 pairs, one for a friend, as he had same problem. He used them immediately, and for nearly a year now. When he 1st put them on he had some sweating due to the different chemicals of the rubber, but over time, and wiping them several times he has since had no issues and they are fine on the figure.
But it's up to you to do whatever you'd like. Just relaying to you what I found and my experience with using the armory boots rather than trying to do the feet swap mod, as I also felt I'd more likely end up cutting and ruining my original boots as well.