if your still on wheezy not sure what to do if you are on jessie normally you normally also need to da a sudo apt-get update sudo apt-get upgrade to update your firmware and update retropie using the retropie-setup script. I believe update retroie pie script and then install from binaries.
however i was still on wheezy and using retropie 1.6 !! so i just downloaded the new retropie 3.6 image and copied over al of my roms en setted up everything from beginning again since i wasn’t sure config’s could be copied without changes.
About save games you’ll have to find out where they are saved (psp / psx / n64 etc think like actually saving ingame not save states) and probably will work again
About save states you’ll also have to find out where they are saved (other emulators) and copy those over.
If for some reason you were using old emulator versions and in the newer versions being used now there have been changes to savestates or save games it is possible if they are not backwards compatible that it won’t work. I have no info on that though and did not try to do this.
My guess is that save states might break quicker then save games (memory card files etc) but not sure if there are changes. if you only have save states it might be a good idea to also make sure you have save games also depening if the system / emulator used these (again think like memory cards used).
i think retroarch emulators show you the location of the save state when you save a save state on the screen, at least it does so with me so for those you can quickly find out where they are saved. Other might be saved in the roms directory or config directory in certain directories all depends on the emulator used though.
you can also install the new retropie 3.6 on a new card already with some of the games where you have save states / save games from and copy everything over and test it before actually doing the upgrade(s) on your old retropie card.
maybe someone else already did this ? but for me i started from scratch to be save