Yes, the networks use different frequency bands. Ostensibly, nobody has yet developed a chip that works on both LTE bands. The iPhone 4S shipped with a chipset

Yes, the networks use different frequency bands. Ostensibly, nobody has yet developed a chip that works on both LTE bands. The iPhone 4S shipped with a chipset that worked with both Verizon and AT&T's 3G bands, so I'm sure somebody is working on the same for LTE. This is just an effect of the technology being newer.