It doesn't matter unless you plan to use Verizon in the states, both will work just as well on T-Mobile, and also abroad. I'd recommend keeping the Verizon one though just to give you the option to go with Verizon later if you choose.
There is no difference hardware wise, the only difference is the ESN from the Verizon one is in their system so they will be willing to activate it if you ever switch carriers. Technically there is nothing stopping Verizon from activating the T-Mobile one, but their policies don't allow it.
It doesn't matter unless you plan to use Verizon in the states, both will work just as well on T-Mobile, and also abroad. I'd recommend keeping the Verizon one though just to give you the option to go with Verizon later if you choose.