Over at the MacRumors forums, reader jsnuff1 has confirmed that the new Verizon iPad works with AT&T's 3G network. The Verizon iPad has a built-in GSM SIM slot and supports connections on the same 850/900/1800/1900 MHz bands as the AT&T unit.
What jsnuff1 did was to slot in an iPhone microSIM, using the standard AT&T APN carrier settings hack, and then test the unit using AT&T's 3G service. You can use this approach for both standard AT&T iPhone accounts as well as the Pay-as-You-Go ones discussed in this TUAW post.
If you take this approach, do not expect to use AT&T's LTE network. Real 4G service (i.e. not FauxG) runs on 700 and 2100 MHz for AT&T. The Verizon model supports only 700 MHz.
The opposite approach will not work. To the best of my understanding, Verizon CDMA does not use a transferable SIM, so you cannot move a Verizon account onto an AT&T iPad.
In the end, what this means is greater flexibility. When you move outside a Verizon coverage area, you can swap in an AT&T SIM and get 3G data service at least, or share that service without tethering but with a little bit of paperclip work and SIM swaps when on vacation.