My Note 3 is Hardware version N900V.07. I actually have not yet experienced network signal loss in my workplace. I mention workplace as its a large multi-story building with concrete/steel structure. 100s, if not thousand or more people work in my building and the immediate surrounding ones. Beyond our office complex, is a busy shopping area and nearby highways. As such, the Verizon network towers are likely getting plenty of use in my area.
I have, however, experienced fluctuations in 4G LTE signal strength, and intermittent/random drops to 3G. 3G is particularly present in the basement areas or where there is more building structure - all of which is expected.
I also have used an iPhone 5S in the same workplace. I routinely get no signal at all when coming out of the basement. I set my phone to Airplane mode while in the basement to prevent excessive battery drain since the 3G signal often degrades to 1x or no signal. I can get 3G on the Note 3 in the basement, but still toggle to Airplane mode. Upon exiting the basement, I always regain signal (3G or 4G) with the Note 3. With the iPhone, not the case. Only a power down/up cycle will regain signal. Have tried with multiple SIMs and on two different 5S. Same results.
So, it may be that the issue with the iPhone 5S and its radio/FW combination and how that interacts with the VZW network is: a bug in iOS 7.1.2, a bug in VZW network that is more prevalent with the 5S, or that I'm just really good at timing the Airplane mode to Off with when the VZW towers are the busiest.
All of the above to indicate that the signal drops for the current Note 3 radios/FW may be primarily isolated to a combination of environmental and network conditions. There is also likely a difference from or impact by the Note 3's new AWS capabilities, and those of VZW network - as reported in this thread and elsewhere.
In summary, this is a guestimation on my part from reading about others experiences coupled with my own.