I did close to 100% on the ps4 but on the pc version I only have like 30% and its the platform that I got phantom pain on.
I have come across a few different conflicting articles that say what actually carries over. One said it was just the POW's where others said it was something about having 100% to get different outfits. I am not sure what exactly it does as I have not started Phantom Pain yet but I figured it was better to have the 100% to not miss anything.
You unlock special suits too that are quite awesome.