How to find the root of android slow down
As far as I now Android device slowdown can occur for several reasons:


Very low amount of free RAM.
Check under Settings>Apps>Running how much free RAM you have
If your free RAM is too low (70-150MB or less) it's probably the cause so check which app/apps, if it's not an app maybe it's a bug in the ROM. (see 3)
Low free space on internal storage. (check under Setting>Storage)
If the free space is too low (~2GB or less), try free up some space and check if that helps
Kernel bug/misconfiguration.
Try to check your CPU usage stats, clock speed, governor, number of active cores etc...
(If you havn't flashed a custom kernel and never changed the governor/clock speed or other performance settings it's probably not the problem)
ROM bug
You can try perform a nandroid backup, then reinstall the rom after full wipe and see how it performs, if it's still slow, try clean install of the version that previously worked fine (only if you know what you doing!)
Bug in one of the user apps.
If your CPU/RAM usage is too high for no reason maybe one of your apps eating it.
I recommend you to try OSMonitor or any similar app to find which app eating your CPU/RAM.
(Lack of TRIM, TRIM does exist in Android 4.3 and up so it's not the problem)
(In some rare cases bad sdcard can cause such problem but it's not the problem too since Galaxy Nexus doesn't have card slot)