Verizon acts like they are doing you a big favor by letting you use their network. I switched from Verizon to T-Mobile because I wanted to be able to use Google Nexus devices. (My last Verizon phone was a Samsung Galaxy Nexus, but Google got fed up with Verizon over how they mishandled the Galaxy Nexus so there aren't any new Nexus devices for Verizon.)
Overall I'm happy with T-Mobile. And it was fantastic when I recently visited Japan and my phone actually worked. It was 2G speed only, but Google Maps worked great, Google Translate worked great, messaging worked great.
There are a few spots I have visited where a Verizon phone gets good signal and a T-Mobile phone doesn't work. They are few enough that I'm glad I made the switch.