Since no two phones are the same, in terms of usage, user preferences, customization, etc., there is no such thing as a "Best _____" for anything. It is more a matter of playing around to find what works for you. Also important is to read, then read some more, gather input from other users (which is clearly more so the aim of a "Best Of ____" thread). Just be sure you know what you are flashing (from recovery) or pushing (via Odin) to your phone instead of jumping blindly, and ALWAYS make a backup first!
That is my two cents on the topic in general; now here is two cents more on ROM's I like personally:
Carbon, as mentioned above, is my all-time favorite, for any device; 4.3.1 worked very well for me and has a ton of customization; can't wait for their 4.4.x builds, which should be here any day
CyanogenMod 11 (CM11) is my current daily driver, it has been unbelievable for me considering that it is a "work in progress;" if you want 4.3.x, they do have a stable 10.2 that was released just prior to the start of their KitKat builds
JellyBAM also has worked well for me in the past, and they have also just started releasing KitKat builds (version 1.0 is their number for Android 4.3.x, version 2.0 is the newer 4.4.x)
Stock/rooted 4.3 from my man JD (jdsingle76) is a must-have for me in order to have a reliable stock build that I can use for various purposes; stock builds *should* be more reliable than AOSP because they incorporate all of the intended features (LTE, MMS, etc.) of the original without any need for a patch