For those of you looking for a super-fast, stable, and the best Android 4.4.2 KitKat AOSP ROM for your Galaxy Note 3, definitely look nowhere else than Resurrection Remix ROM.
Resurrection Remix ROM by XDA user WestCrip has been around for a few years now (since Galaxy S2), and it’s one of the best AOSP ROMs that have proven track record along with a slew of customization/features you will be very happy about.
First, this is an “AOSP” ROM (What is AOSP?), meaning it runs pure Google Android OS, not TouchWiz. So, you will lose all of your magical Samsung TouchWiz features like multi-window, Air View, S-Pen, etc…etc… BUT, you can still use features like IR Remote (by using 3rd party apps) and there’s a ton of S-Pen alternative apps you can use on the Play Store (See S-Pen Alternative Apps).
You can install this ROM on any Qualcomm-based Note 3 such as AT&T SM-N900A, T-Mobile SM-N900T, Sprint SM-N900P, Verizon SM-N900V, international SM-N9005, Canadian SM-N900W8, and more. But DO NOT INSTALL if you have Exynos-based SM-N900 as you will HARD BRICK! For AT&T and Verizon, you need to have the developer’s edition with unlocked bootloader to install, WILL NOT WORK WITH SAFESTRAP at the moment.