Unlocked Verizon/Sprint phone can be used on AT&T... fully?

Referencing the FAQ here (http://www.apple.com/shop/iphone/iphone-upgrade-program)

Are there differences between an iPhone for AT&T or T-Mobile and an iPhone for Sprint or Verizon Wireless?

iPhone offers the same innovative features regardless of the wireless carrier you choose. If you choose AT&T or T-Mobile as your wireless carrier, your iPhone will use 3G cellular technology for voice services and either 3G or 4G LTE cellular technology for data services. iPhone can roam internationally on many GSM carriers around the world. If you buy iPhone with AT&T or T-Mobile, it will not work on Sprint or Verizon Wireless.

If you choose Sprint or Verizon Wireless as your wireless carrier, your iPhone will use CDMA cellular technology for voice and data services. If you buy an unlocked iPhone with Verizon or Sprint, it will work on AT&T or T-Mobile. An iPhone activated on Sprint or Verizon Wireless also has the ability to roam internationally on GSM networks. For details on LTE network support, please see www.apple.com/iphone/LTE.

Why would someone NOT get an unlocked Verizon phone then? I compared the bands listed on the LTE page, and they're identical.

I'm thinking the only difference is non-LTE. While the page says "it will work on AT&T or T-Mobile" should there be some fine print saying "only if using LTE service" - or am I missing something here? Seems like getting an unlocked CDMA phone would make more sense, to be able to switch back and forth, but I think there's some missing fine print about the fact that non-LTE won't work at all (right?)