Couple of things to note, when you duplicate a comp. First, you need to do your duplication in the project panel. If you are inside a comp, and duplicate a precomp, you haven't created another asset, it's just the same asset twice.
The other thing, is if you duplicate in the project window and your comp has multiple precomps---they haven't been duplicated, just the final comp---so if you change those precomps, they will change in the old master aslo. All the precomps need to be duplicated also, then dropped into your new master.
For me, I find True Comp Duplicator to be one of the best scripts out there, completely takes the work out of duplicating and replacing assets. Select your master, run the script and it makes a complete new master, with completely new precomps.
Johnny Cuevas, Editor
"I have not failed 700 times. I have succeeded in proving that those 700 ways will not work. When I have eliminated the ways that will not work, I will find the way that will work."
---THOMAS EDISON on inventing the light bulb.