I don't own all three devices, but I can share my experience on why I chose the Moto X.
I was using a N4, but I was considering between the N5 and Moto X, I went ahead with the Moto X due to their recent sale.
-Despite N5 1080p screen, I like AMOLED screen for better contrast and dark level, I tend to use the phone in bed in the dark (don't ask), I can't stand backlight leakage and poorer contrast of some LCD screens.
-Moto X general perceived better battery life
-Touchless control
-Better build materials (imo)
-Phone size is just right, I dislike oversized phone
-For once I want to support an American company instead
I don't know if it's the right decision yet, since its all about software for me and I can do unlimited things with the N5 such as installing a custom kernel that allow things like: swiping across the screen to wake/sleep the device, fine tuning the display or sound chip, multiboot into multiple Android roms and Ubuntu and other Linux OS. I will miss these things, but nowaday I mostly use stock Android and only need root. I do know Moto X is supported by Cyanogemod so eventually it will get some features, but it won't be as abundance as a Nexus. It also lack qi charging which lose a coolness factor.
I'm trying to look at it in a practical use and I think the screen, size, battery life and features of the Moto X might be more useful for my case. I can do a lot of things with the Nexus 5, but in the end of the day its more about tweaking fun than actually using the phone. Personally I want both phones, my ideal phone right now would be the Nexus 5 with AMOLED screen and the Moto X power saving processor and features. Or inversely you could say I would like a Moto X with 1080p AMOLED screen, qi charging, and is Google Edition.
As for the Note 3, I hate big phones, I wouldn't touch Touchwiz with a 10ft pole, I dislike Samsung build quality for recent devices, and it's too much to spend for an unlocked one.