How much of a performance drop could result from installing games on a HDD?

Any game that loads a lot of assets when switching between zones/levels will suffer. Games that load everything into memory all at once at the start are good to go. You will notice stutters/longer loading screens when switching between these storage reads, but moment to moment gameplay won't see much effect at all unless the developers were dumb enough to load assets from storage instead of memory constantly. I can't really pull specifics, but stuff like skyrim will literally be 5-10x faster at loading screens, loading a multiplayer map for a live service game also in that ballpark. Then again I had a terrible HDD at the time, if you have a modern one you should expect up to double, see below: