I think people need to understand the difference between first generation AMOLED and latest Super AMOLED panels used. Moto X has the same panel used in Jet or Wave, which will look great as they will be vibrant and rich, but WAY OFF from true / natural colours. But this has been sorted out on S5, I still believe it's the best phone for display out there (kindly read worthy reviews like of Anand and all), it keeps the main advantage of AMOLED, like keeping the superior contrast ratio and deeper black levels yet matching the true and accurate colours. I have spent hours and even at a time was literally obsessed about calibrating my TV (VA) and monitor too (IPS) to match perfect dE, and I did too, but in the end I realized while watching movies or playing games, you know what matters, the only thing? Contrast ratio and vibrancy of colours. You won't give a bloody damn about accuracy there especially when you will see washed out black levels of IPS (which looks disgusting in movies to be honest) and dull yet accurate colours. Unless one want to do photography related editing work I don't think there is a huge advantage of IPS (kick TN out of the competition please).
In you cell phone you are not gonna do any photography related work right? Those IPS displays, for example Z2, look what Sony did with the white balance and gamma, they changed it to match the vibrant colours of AMOLED panels, so it's basically a IPS panel with over-saturated colours. The near perfect IPS panels would be G2 or M8 or those kinds, and when you will see it in front of Z2 or S5 you will say, hmm, colours look washed out.
Anyway, too much lecture here I guess. I will choose Moto X over S4 thousand times. TouchWiz sucks big time, I don't know how Samsung managed to create a heavy and bloated skin as that, so just for the sake of software optimization Moto X will thump and blow the S4 out of the water as many times as it want, even when it is running on inferior hardware. And believe me, in a cell phone all you will care about is the software optimization part, that's why devices like Nexus or Moto X has so much praise, and I respect that, even when the former has a cheap and poor build quality with a below average camera, and latter an average camera and inaccurate display.
So at the end, the S4 wins in two categories only, the camera, it's good, it's capable, no matter what people are saying, the HDR mode is brilliant, however forget low light shots, it's million times ahead of Moto X and N5, and the display too, you can use a custom kernel to make the display more saturated (I personally used the movie mode at the end), but that's about it. All other points are in favour of Moto X. Now you decided as per your priority.
However being said all above, one thing I am slowly understanding, there are small things which matter. Samsung devices might not have all the basics right, like disgusting vibration (however believe me there are very few device with decent vibration), putting that tiny mono speaker grill at rear side, but some of there software modifications are rather handful, like now with my M7 I don't see any scheduled messaging, also when you go to call history on Samsung and tap on a log it shows you the history, while on M7 if you touch on a call log once it will dial that person, you will have to press and hold to see the history, which is ridiculous and utterly time wasting. These small and tiny things will never be mentioned in any review, but only time will give you the idea of these things, and they all matter.
Remember one more thing, Moto X might have a locked bootloader, so you won't be able to root it, unless you purchase a dev edition without warranty. I don't get the purpose of an un-rooted Droid, and never will.
