The hardware on ALL iphone 4S models appears to be EXACTLY the same. At present moment, I'm holding a Chinese model iphone 4S (A1431) that is supposed to be GSM hardware only with zero 3G capabilities and intended for use in China. The handset is cracked and running on AT&T with a nice 3G icon next to it right now. (I didn't do this feat, so please don't ask for assistance if you live in China on how to crack your GSM only iphone to 3G)
I also happen to have my person iphone 4S from Sprint that has a curious thing about it.... the firmware version + carrier. On an unlocked phone the Carrier will be listed at 11.0 and on Sprint, the Carrier is listed as 11.1 (Sprint). My gut feeling is that the firmware on this device may be 220.127.116.11 or 18.104.22.168, but that the carrier is also installed in the firmware to the handset and not officially changeable once flashed by Apple initially at the factory (excluding OS upgrades).
This Sprint iphone 4 behaves differently that an unlocked iphone 4 with the same OS version. My company pays Sprint a crappy $40 per month tethering fee to have the Hot Spot feature and the icon to enable "Personal Hotspot" will not pop up sometimes until the phone is on the Sprint network and has a chance to connect to what I'm guessing in the Sprint server to verify that I have the service allowed and paid for before the icon is allowed to be shown. On an unlocked iphone 4, the option for "Personal Hotspot" (WiFi hotspot) will always pop up immediately in settings, regardless of which network I'm connected to in the world. On a Sprint flashed firmware, this option will not always pop up, especially while in another country with a foreign 3G SIM in the handset, even though Sprint swears to me that they have fully unlocked my personal iphone 4S, so that I can use all features. Sometimes with bad Sprint data network connectivity the blasted icon never pops up, because it never gets authenticated and so the handset has to be shut off and restarted for the icon to be available again (According to Sprint tech support)
My exhaustive point above is to point out of that YES, the iphone 4S on Verizon and Sprint is very likely 100% the same hardware and could be made to work on either Sprint or Verzion, if the carriers allowed the MEID to be registered on their CDMA/EVDO network and had some provision to change the Carrier firmware or it may be a simple server switch. To do this without carrier cooperation, you would likely need the firmware in the handset that belongs to that network along with an with an IMEI that looks like a valid iphone Equipment ID on that CDMA based network and then all should be good. You would also need a Verizon or Sprint mirco-sim for roaming purposed to GSM outside the US. I once heard a story of a man who registered his CDMA modem to Verizon customer support as a normal phone by calling customer support across his laptop headset and telling them that it's 'obvious there is no way I can be talking to you across a modem card, so let's add this voice phone with unlimited data to my account'
I think it is sinful for a carrier to make you commit to a 2 year contract or pay full handset price without the ability to take your handset to any darn network that you choose. Imagine if you bought a new car that could only be gassed up at a Shell gas station and no other place? People would be up in arms! I would encourage anyone here to write to their Senator or Congressman and demand that if people are made to pay full price to buy their handset where the carrier is not subsidizing the cost, then they have no right to exclude inter-operability between networks. You are already paying taxes every month for number portability, so why can't this be expanded and use the same tax for equipment portability as well. It's shameless that I invest $700+ in a handset that is not ever fully mine.
[Disclaimer: I have been acting as a wireless test engineer for more than 10 years, however this fact alone does not mean that my assumptions in the answer above are correct. Best of luck.]