In general, the 4.4 ROM's are going to be a little more "buggy" when compared to a custom TW 4.3 ROM. From my understanding of this it's due to the devs being able to use the official OTA as a base and just customize it. I've ran both and prefer the custom TW 4.3 ROMs. To each their own however.
If you want to stay as close as OTA as possible, scrosler has posted a 4.3 ROM on the Verizon Samsung Galaxy S III Android Development thread. It's titled, "[ROM][1/27/14] - Stock Rooted Knoxless - VRUCML1 - Android 4.3 - Stay Classy XDA!". I'd link you but don't have that ability yet on the forum.