After installing the OTA. Seemed a little laggy at first but now that apps are updated and whatnot, it seems to be smoother. Noticed a drop in RAM usage too.
My phone is much faster with KitKat, RAM usage is averaging about 0.75 - 1.00 GB, my wi-fi signal is much stronger, and the battery seems to drain slightly less than before. Also in the lock screen, I can now operate the camera just by swiping my finger over the icon. All the specs on KitKat work just as intended, no issues as of yet.
It makes sense to VZW. They want customers to buy the Note 3. If they (VZW) update the Note 2 to KitKat (4.4), lots of VZW customers won't buy the Note 3.
I just received mine for Note 3 OTA. it would not download on 4G but on WiFi it started even though update advisor and Keis both said I was up to date. Chattanooga TN area
I know the phone itself is running fast and smooth, but it seems that the KitKat update has also boosted internet speeds, or at least 4G LTE speeds.