First two phones I had were 310k, both had faults and had to download the patch before using the phone.
My third phone is 311k, no faults and it came with KitKat preinstalled (no patch to download)
To check what build (batch) you have, look on your box where it shows the model #, imei # etc and look for S/N. The first 4 characters = build #.
I'm going to try and keep a log of all the build numbers and see if there are any changes to the phone like with the Nexus 4.
So.. so far:
310k - Need to install KitKat - Seems to have quality issues from my experience
311k - Preinstalled KitKat - Quality control seems better
This is just based off of three phones though. More information is needed.