I would absolutely recommend backing up all saves that you want to keep. I have never found a consistent answer on what does and does not migrate or format whenever you upgrade or swap HDD. I would recommend getting PS+ for a month so that you can push all of your saves, including protected non-transferable ones, to the cloud.
If I remember right, and this is what happened to me the last time I tried to upgrade my HDD after I had a hard drive failure with an original model PS3, if the PS3 detects a hard drive change, you have to format, even if you put the original HDD back in.
I know that there is a backup utility somewhere in the PS3 menu, but you will have to use another external hard drive to do the back up with, then install the new HDD, format it, and then recover from the external backup. The reason I suggest PS+ is that it can alleviate the need for the external drive.
To summarize, from my experience and understanding, there are 3 storage devices:
- The current HDD in the PS3
- The new HDD that you want to install into the PS3
- The external drive that will hold the backup
Backup to the external, swap the drives, recover from the external. The external will never be installed into the HDD bay of the PS3, it will only be used to backup data. Remember, format === erase. Bear that in mind.