Turns out I wasn't the only person that's been interested in this. There's an article on MacRumors that states that this is indeed possible, which is good news for me. The person that discovered it wrote:
Big question on everyone's mind buying the Verizon iPad was whether data from AT&Ts 3G network would work on this iPad, or if Verizon/Apple would block this.
I was one of the first to obtain a Verizon iPad and can happily confirm that this is allowed! I used my ATT iPhone 4S sim card and took out the Verizon sim, and data worked! You must apply the AT&T APN carrier settings before this works though.
BTW APN carrier settings can be changed here: unlockit.co.nz
edit: I just tested this and it works. Changed the APN, put my iPhone SIM in, and it worked.
Yes, the two models are physically different. The radio is different.
As per Apple's website, the radio frequencies aren't the same. The verizon iPad supports Verizon LTE, and as per this post, AT&T 3G. However, the Verizon iPad does not support all LTE frequencies that the AT&T iPad does.
From Apple.com:
Wi-Fi + 4G for AT&T model: 4G LTE (700, 2100 MHz); UMTS/HSPA/HSPA+/DC-HSDPA (850, 900, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz)
Wi-Fi + 4G for Verizon model: 4G LTE (700 MHz); CDMA EV-DO Rev. A (800, 1900 MHz); UMTS/HSPA/HSPA+/DC-HSDPA (850, 900, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz)
Notice that there are some differences between the listed frequencies. They're nearly the same, but not quite.
Edit:
To confirm, the difference is a hardware difference, not a software imposed limitation on AT&T LTE. From the Macrumors article:
The Verizon iPad hardware supports only the 700 MHz band for LTE to match the carrier's technology, while the GSM version sold for use on AT&T's network supports both the 700 MHz and 2100 MHz bands as used by that carrier.
If you're looking to travel internationally, go with the AT&T iPad. (I got the Verizon iPad because I wanted the free hotspot feature, which AT&T does not offer for free at this time.)
Best Answer
No.
The LTE standard uses different frequencies in the US and Europe. However, the model sold in Europe is the US model. This has been officially confirmed by Apple [1, german].
LTE in the iPad
The iPad supports only the frequencies 700 and 2100 MHz [2] for LTE use. These frequencies are not used for LTE in the EU.
If you take a look at the footnotes, Apple states on their website (US and foreign) that:
LTE worldwide [3]
The following frequencies aren't really such even numbers. They are frequency bands that spread out over a whole spectrum of which little fragments are divided among carriers.
There also exists this table [4] which lists very detailed information on frequencies bands used world wide. You can see here that the the 2100 MHz band is used for UMTS and IMT (= 3G standards) in Europe. The 700 MHz band does not seem to be used by carries in Europe.