The average person isn't doing what you're doing, they're just copying a file from the old folder into the new folder. When they launch it, and the game tries to use the save from appdata, the game shows errors. It sounds like you're deleting the saves in appdata which prevents the error, but that's not a step people are taking here, nor is it necessary at all since renpy does this automatically.
If you copy it to the correct place, it looks at both, and shows you all of them. the only time it could be an issue is if not all of the save files are not the same, which should never happen, unless you saved in the same slot, but overwrote it somehow, but this is almost impossible to do in normal use. The appdata files and the save folder files are identical, you can copy them back and forth, without issue.
It might check the appdata first, but as long as there is one in either place, it will read it without issue.
I only delete the ones in the appdata occasionally, when I drive gets full or I just get a bug up my ass. The computer I am using now has almost 20k saves in the renpy appdata folder (hanve't cleaned it in a while), it is over 7gig, and all of those have duplicates in the game folder too. No matter what I do, deleat them or not, it never causes a problem. It is made to have them in both places.
The one in the appdata are not the main ones, and are not there to be the main use, it is there for backups, in case you mess up and delete the whole game folder without thinking.
It's made for this, so unless you put the folder in the wrong place or have two different saves in the same slot, it shouldn't matter either way.
It isn't necessary to copy them over, unless you have a windows crash, and lose your system, or the drive fails, or... How often do we have people come in here complaining that they lost their saves even with that backup system? I mean, many are lying, and just don't want to play, but still, I assume most are being honest.
Point it, it never hurts to have spares. Same reason I am on page 30something here on saves. You can't have too many spares.
Sierra On-Line Motto: Save Early, Save Often.