I have hotspots from all 4 carriers, and I have and iPhone 5 on Verizon and a 5S on T-mobile. Verizon can get congested, so you may be paying the price in slow data speeds sometimes, even though there's a signal in most places. Fortunately their recent addition of "XLTE" is helping to mitigate some of these problems now.
T-mobile really does have "the fastest network," like they advertise, but you need to check coverage where you live. There are a number of locations around me where it's literally 5-10 times faster than Verizon (but Verizon still wins a few other places, and occasionally can even match T-mobile's fast speeds). When I say fast, I mean around (or over) 30 Mbps both up and down.
Also, both T-mobile and Sprint have minimal spectrum implemented in the low bands (e.g. 700MHz), so indoor data coverage can be problematic at times (slow speeds in some buildings). At least T-mobile helps compensate for this by offering both WiFi calling and a free (with $25 deposit) Cel-Fi unit that will boost the LTE signal inside of your home.
Sprint advertises "the newest network," which means it isn't developed enough yet! It has its strong points, but for the most part I wouldn't consider it for at least another year or so. Also, Sprint iPhones (even the 6 and 6+) are pretty much locked to Sprint.
With T-mobile you won't be on a contract, so you can switch back to Verizon if you don't like it. Just pay off your iPhone, unlock it, and switch to AT&T or Verizon.