Correct me on this if needed, but all Verizon phones are sim unlocked and work with GSM per FCC agreement. So you could get that version, but I would check it first when receiving it to see if it work with a GSM sim, if not you can get an RMA for a refund. The Verizon edition have the 3G bands to work with ATT, it lacks T-Mobile AWS 3G band (1700). Also it only support LTE band 13, it doesn't support LTE bands 2, 4 or 17 that come with the GSM unlocked version, so you will not get LTE on ATT or T-Mobile.
There is zero reason to get the ATT version what so ever, none, zilch. It's sim locked (though you could ask ATT to unlock it I guess), cannot unlock bootloader. The T-Mobile version is actually the unlocked version, it support every bands required by ATT, both 3G and LTE. T-Mobile version have unlocked sim and bootloader, doesn't have carrier logo nor carrier bloatwares.
Then there is the unlocked GSM Developer Edition which allow you to unlock bootloader without losing warranty, is similar to regular T-Mobile unlocked edition, except that it lacks T-Mobile AWS 3G band. You can get the Dev edition for Verizon as well which have the same bands support as the regular Verizon version. You can not unlock the bootloader for the regular version of ATT and Verizon.
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