I updated my iPhone 5, and 6.1 is working fine. Although, I can't say the same thing about the new carrier settings that it asked me to download. For some reason, my phone keeps dropping from LTE to 3G for no apparent reason even though my signal strength was high (3-5 bars).
Last time, I turned it to airplane mode to get LTE back, but I didn't wait long. This time, I left it alone, and LTE came back.
I'm wondering if the carrier settings are designed to drop LTE connectivity if you're idle for too long. My only thought is that Verizon wants to keep their LTE stations from becoming too saturated (LTE is limited to 200 connections per station per 5Mhz). Since my max transfer speed is only 20Mbps, I'm assuming that Verizon only implemented a 5Mhz setup here. Although, thinking about it more... the phone may be dropping LTE to avoid wasting battery power keeping it active. The iPhone has to keep a CDMA connection active at all times or else you can't receive calls or (non-iMessage) texts, and if you have LTE enabled, it also has to keep that connection active as well.
In other words... go go, VoLTE!