In the past few weeks of using my S3LTE in my various travels, I've discovered that the S3's LTE radio (and/or antenna) is pretty much crap. I'll get terrific throughput (well, relatively speaking for Verizon's oversubscribed LTE) on my Nexus 6 phone, but on my S3, throughput will be much lower. And quite often, I'll have zero LTE service on my S3 while I have plenty of throughput on my N6.
Plus, when I'm on the train, and I lose LTE signal briefly (when the train enters a VZW deadspot), my N6 will pick up LTE without problems, but the S3 will struggle to reconnect. Oftentimes, turning off/on the S3's LTE radio is the only way to convince the S3 to reconnect.
I bought the S3LTE thinking that it would be so much more convenient to have an "always on" LTE connection, but I've since learned that this dream is not reality. Turning my N6 into a personal hotspot and connecting the S3 to the N6 via WiFi is WAY more reliable then trying to keep the S3 online via its built-in LTE radio.