Is the Verizon iPhone 5 compatible with T Mobile?

Hi, my girlfriend has an iPhone 5 and we are currently on Verizon.

While we don't have any complaints about the service, their plans are rather expensive and I know that the iPhone 5 is sold unlocked through Verizon. So I was wondering if we were to just pay the ETF and get on a T Mobile prepaid plan, would we be able to use T Mobile's "4G" speeds? Or would it be stuck on 3G or worse, EDGE?

Also, would you consider this to be a good or bad idea?

i've tried Googling it but all the articles I've read only say that it would work on AT&T LTE and "might" work on T Mobile.