Well the difference is that this is NEXUS device and is AOSP supported. So 99.9% of the ROMs that come out for this phone are stable. They're not stable on the S3 for AOKP/CM right away because they have to actually do work to make it work; whereas, N4 is AOSP supported and its like.. BAM! it works out of the box. As for S3, the phone ships out with TouchWiz. Going from TouchWiz to AOSP requires work to make everything work.
I'd say CM/AOKP are pretty stable overall. All ROMs are stable. This is one of the many benefits of having a Nexus device and I don't believe in when people are wanting to upgrade and people say "oh just get a S3.. it doesnt have latest but just flash a custom rom and you'll be on latest android) no it doesn't work that way just because of like what you said... instablity. When Android 5.0 (Key Lime Pie) comes out, N4 will be one of the first devices to launch with it and we'll have the most stable ROM day one without having to rework code to make all the functionalities like calling, 3G/4G, WiFi, Bluetooth, Screen Rotation, Data, etc to work (I know on other phones, people release dirty ROMs and things like what I listed don't work as of yet until its fixed)
Shopping for a ROM/Kernel is like shopping for a car. Some tips to take,
1) Browse the original and android dev forums. Search around and look for whats interesting.
2) Find it interesting? Read OP post and the past 6-7 posts (dont even read it.. skim through it for feedback)
3) Like what you see? Check for screenshots or even a YouTube video
4) Still like it? Flash it and try it

and most of all, ENJOY.