Glad you were able to do it, confirms my suspicion that the phones are actually identical but the software image is different. Not unlike how you used to be able to flash international 920 ROMS to North American 920's to enable different bands (I know, not the same since both are GSM). I'm no expert, but I'd imagine Qualcomm radios (on the Snapdragon) can physically handle both CDMA and GSM/UMTS/LTE but they disable the CDMA capabilities in the image, either through software or physically disabling it. Given the AT&T and Verizon iPhones are now the same model (at least by model), I'd imagine this applies to their stand alone radios as well. Its simply cheaper to manufacture one product in mass instead of all the different variants.
Did you notice any differences when you swapped them?