There are shitty Chinese knock off controllers ofc, but the battery dying in a PS3 controller is super easy to rectify. I would recommend replacing the battery before trying a knockoff.
I would have thought that the vast majority of people who download ROMs download them individually based off of their preference, not downloading the entirety of the PS1 or PS2 library.
To answer your question, it doesn’t matter other than compression. Backups are backups.
THANK YOU