As many have already stated, I would first check to make sure you get adequate coverage from AT&T in your area. Having LTE coverage would obviously be the best case scenario, but if you don't have that, then you should at the very least make sure you have HSPA+ (or "4G") coverage with an iDevice.
If you have good coverage in your area, I would visit an AT&T store and explain to them that you are a VZW customer looking to switch. But make sure to mention that you have unlimited data plan with VZW and make sure AT&T will match that before you make the switch.
I'm not sure what AT&T's policy may or may not be regarding individuals in this situation, but I would be inclined to think they may work something out with you. If they will accommodate your unlimited data plan and honor your corporate discount, then I would do it.