When everyone goes to LTE, all the damn bands will be different, and it's still the same thing, different day
This is where it's going to be righted.
Verizon uses the 700mhz band for LTE right now. Cell phone makers are already combining phones with AT&T and Verizon's 700mhz LTE bands. This is something you didn't see a year and a half ago.
Verizon is going to, this year (if they haven't already), start deploying LTE on AWS. AT&T and T-Mobile devices that support the AWS LTE frequency will work fine on Verizon's LTE.
Verizon has in place a roaming agreement in place to use Clearwire's 2.5ghz LTE network once it's up and running. This will (likely) belong to Sprint sometime in the next year and will be where they go to expand their LTE network once they finish their 800mhz deployment. This means Sprint phones will have this band and a Verizon SIM should work just fine on those phones with the (likely very limited) Clearwire LTE deployment.
Verizon has also announced their intention to begin refarming their 1900mhz PCS spectrum to LTE sometime beginning in 2015. AT&T and TMobile will likely begin doing the same by then, in anticipation of VoLTE, dedicating more and more bandwidth to LTE. This means those devices will also end up supporting Verizon's 1900mhz LTE deployment.
The point being, by the time 2016 rolls around, Verizon's spectrum holdings and agreements should overlap with just about everyone. Once VoLTE becomes the norm for all carriers (2015?), Verizon should be able to take just about any phone from any other carrier in the US.
What I find most interesting about Verizon's spectrum moves is the thought of how much longer they'd need to keep using the 700mhz C block. Once they start refarming the 1900mhz spectrum, I'd suspect they'll start deemphasizing their 700mhz holdings, in an effort to... alleviate themselves of the FCC's block C open access and open applications requirements. But who knows?
EDIT: Not that I'm advocating staying with Verizon if it doesn't make sense for you. But, if your only complaint is device compatibility, that situation is going to get better every year.