Just got my Moto X a couple days ago. Came from a launch-day S4 running AOKP. No complaints, I just wish I had root on the X.
Lag: I turned everything "S" off on the S4 when I got it, and never experienced lag. When it had AOKP, no lag either. The Moto X does not lag, either. As far as I am concerned, it's a wash, but YMMV.
Battery: Just about the same. My usage pattern is very consistent. Both phones make it through my day with about 20% left.
Performance: I don't care what the benchmarks say, they do all the things I need them to and I don't feel one was faster than the other.
Screen: I could never tell much of a difference between 720p and 1080p. Not enough for it to sway my decision one way or the other, that's for sure. My past 6 phones or so have all been AMOLED. My tablets have been non-AMOLED, and I can say I much prefer AMOLED.
Camera: The stock S4 camera was pretty good, but I was not a fan of the software. The GPE and AOSP camera's both kind of suck, in my opinion. The GUI/functionality is great, but I always find the shutter speed to lag and it is almost impossible to take decent pics. Focus (the cyanogenmod camera) was what I started to use towards the end of my time with the S4, and it is a pretty solid camera app. The Moto X camera does take some weird pics sometimes, but more often than not, for me, it has taken good pics. Once the Moto X update is rolled out to everyone, I'm sure it will be about a tie.
The Feels: Moto X wins this by a mile. The S4, especially with a case, is just too big for me. The Moto X just feels amazing in your hand. It is just about the perfect form factor.
Time to sell the S4.