The Verizon OTA update is a firmware update. The difference between NC2 & NC4 is that the first was a leaked non-official bootloader. The benefits that came along with it were the ability to flash backwards to previous bootloaders, and some unique possibilities related to the kernel. Once on NC4 you cannot flash backwards, but the NC2 kernel can be flashed on top of the NC4 bootloader so that it retains all the benefits of NC2 except the ability to go back from kitkat to jellybean.
NC5, which you have provided a link to is an S4 firmware, NC2/NC4 are Note 3 firmwares. If odin even let you flash the NC5 tar it would at the very least soft brick your phone.
I would say that unless you want to go back to jellybean at some point there is no reason not to be on the NC4 bootloader with NC2 kernel as NC4 is the official bootloader, however the opinions across the forums may vary. What is clear is that taking any OTA update is unwise if you want to maintain root access to your phone. This community is full of developers that dedicate their time to providing us with a way to keep our phones as close to the way we want them as possible, for without them we would be on our own and many of us would never experience the possibilities. Thank God for devs.
I hope this helped.