Now that AT&T is finally ramping up it 4G LTE network to catch up with Verizon, you might think that you'll soon have more carrier options or roaming freedom if you pick up a 4G LTE handset. This, however, is not true. Verizon recently confirmed that its LTE phones will not be compatible on other LTE networks in the US.
Although the new 4G LTE system runs on SIM cards much like how we're used to with GSM networks, which leads one to think that its possible to simply swap one LTE handset for the other, the incompatibility has to do with differing frequencies between the two carriers. Verizon's LTE network runs at 746-787Mhz while AT&T's LTE network runs at 704-746MHz. There is some overlap, but not much.
Additionally, Verizon still uses its 2G/3G system for routing voice calls while AT&T uses GSM/HSPA. This means that both networks will also have to transition to fully using voice-over-LTE before they can be compatible.
It's possible for carriers to build phones that can accommodate both Verizon and AT&T's frequencies, but since having exclusive handsets are part of how one carrier distinguishes itself from another, it's unlikely either carrier will be motivated to do so. And even for purposes of better roaming coverage, it will still require some new deals to be inked between the two companies.