I'm a Verizon customer and I set up my unlocked phone this evening. I went from a Verizon locked Galaxy S6 edge to this phone. The only thing that I even noticed during the transfer process was that the Verizon voicemail app was specific to their phones. I wasn't aware of that, but since I don't get many voicemails, it didn't matter to me. I found a third party app in about 20 minutes and recorded a standard greeting and everything is rosy. The other Verizon apps (Tunes, Naviagtor, Cloud....etc...) I never even opened on the old phone. Everything else carried over seamlessly, even my text messages, which I was ELATED to see. Smart Switch is your friend.
So - I suppose the answer to your question really depends upon how much YOU use Verizon's specific apps. If you're like me, and never even launched them, then an unlocked phone is fine. But if you rely on any of them (particularly the voicemail and perhaps the cloud), then you may want to stick with the locked phone. Weigh those pros and cons.