Natural immunity from Covid is better … really?

For all „TL;DR“ fans: „Yes, but …“

There are several videos and texts on the net which refer to studies from Israel and others and state that the natural immunity against Covid (i.e. a survived infection with the virus) works better against a new infection than that acquired by vaccination. The studies mention factors between 8 and 27 times. But while some reports are at least halfway factually and technically correctly, vaccination opponents use the information for their misleading propaganda, as usual without really extensively thinking about the problem …