Can a Verizon iPhone 5s use T-Mobile LTE?

I'm planning to purchase a new iPhone 5s outright (ie, not on contract) for use with one of T-Mobile's prepaid plans. I'm wondering if it makes more sense to buy a Verizon iPhone 5s, just in case T-Mobile's service is unacceptable. I know that Verizon phones come unlocked, due to the terms of a recent spectrum purchase, but I don't know whether that applies only to the 3G bands. I also know that if I buy an unlocked T-Mobile iPhone, Verzion will not allow it to be used on their service. Does anyone have experience with this? I'm certain the Verizon 5s will work on T-Mobile 3G/HSPA+, but I'd really like to have LTE.