I followed this guide here: UPGRADING A PS3 SLIM HARD DRIVE.
The upgrade itself went quite smoothly, and everything appeared to work fine, that is until I actually loaded my save game in Skyrim. Prior to the upgrade, I had the Hearthfire expansion installed and the last point I saved at was outside my house that is made possible via this expansion. Lo and behold, the SSD upgrade made my house disappear! I thought I was going crazy for a while, and checked the map a few times, but no, the house was not there, looking for it on foot didn't find it either. Weird I thought.
Where the house used to be before, now was a barren land. Most of the items I owned were in that house and now potentially lost. Bummer right?! Well, then I thought to check the DLC menu in Skyrim - it told me there was no downloaded content! I went back over to the Playstation Store and redownloaded Hearthfire. Once that was installed, the house and all the items were back.
I don't know if this applies the same way to PS4 or any other games, but I was under the impression that the backup utility would capture everything, apparently that is not the case. So this is something to watch out for.