Is the 3rd generation iPad carrier locked in the US to either Verizon or AT&T? Can you swap out SIM cards between Verizon and AT&T?
Effectively yes - you should not expect to be able to use a Verizon iPad on an AT&T account or the other way around. The next two paragraphs only apply to the US iPads.
Internationally (outside the US), the micro SIM slot is unlocked, so you will be able to insert a non-AT&T/non-VZW card in either and have service without needing to jailbreak the device.
See: http://www.apple.com/ipad/4g/ - the section on selecting a carrier and ready to take on the world.
It appears that you can use an AT&T SIM in a Verizon iPad, but the reverse is not certain yet.