Install Nexus Android on Samsung S4
Yes; The Nexus Android is closer to AOSP which is a minimal OS all the other Android distributions are built on. You probably want CM though as it's the most popular pre built ROM for your device.

https://wiki.cyanogenmod.org/w/Jfltexx_Info

Also unlike the Samsung ROM, CM gets security updates every month and unlike Samsung will continue to for older devices like the S2, S3, etc.

https://en.m.wikipedia.org/wiki/AOSP