Since this is a Note 3 forum, it would be great to have this thread for reports on Verizon's Band 4 LTE, and especially Speedtest.net results which should be north of 100Mbps!
Similar thread exists in GS4 forums: http://forum.xda-developers.com/show....php?t=2502716
And a much more in depth one over at HoFo: http://www.howardforums.com/showthre...te-Radio-Units
This article also talked about Verizon's 2x20Mhz AWS LTE: http://gigaom.com/2013/10/14/watch-o...-stirs-in-nyc/
On Galaxy phones it should be easy to access ServiceMode via dial codes, which will allow you to monitor the Band you're connected to, and even force the certain frequency. I don't own Note 3, but afaik Verizon usually tries to block out these codes, although there used to be an app in Play Store that would dial the codes for you (Samsung ServiceMode or Sammy codes)
*#0011# General Debug screen
*#2263# Allows you to force any frequency on your phone
*#27663368378# Main screen
There are a few other codes, please post your findings!