I have both an iPhone 5S and an iPhone 6 active on 2 of the lines on my account and they work just fine.
Sorry but that's just not true. I have 2 iPhone 6S Pluses, an iPhone 6, and an iPhone 5s in my household all using the Verizon network with no issues at all. No problems traveling either. Millions of others are also using theirs on the network so clearly In general Verizon isn't having an issue with their network handling the phones.