After having used this for a couple of weeks now, I just wanted to say thanks to Beans. I'm not going to claim to know exactly why this is better to use than the stock ROM, but I assume it's a little more efficient. (afterall, this is my first Android phone since my original Moto Droid and I've just switched back from iPhone.)
I chose this ROM mainly because it keeps Samsung's look and feel. I seem to be in the minority, but from a design aesthetic standpoint, I think that AOSP's looks are a little lacking to say the least.
Samsung Galaxy Note 3 - Verizon