It's not a really old property - ~200 year old townhouse converted to flats about 120 years ago.
Walls are roughly 1m thick sandstone.
I live in one of the older apartment buildings in SF, built in 1907. (Not much exists older than that, for... reasons) I can tell whether my upstairs neighbor drops a quarter or a dime, and I am regularly woken up by the next door neighbor's iPhone alarm clock. The whole building shakes slightly whenever a Bart train (which is pretty far underground) goes by.
Walls are roughly 1cm thick plywood, apparently. And yet it still costs a fortune!
I live in a 100 year old brick tenement in Brooklyn, though, and hear very little of our neighbors myself— occasional creaking floorboards, and some sounds from the staircase near the front doors, but that's about it.
I'm in an older (~1930) building in Belltown and have only heard my neighbor above me one time (I think a chair fell over or something). Honestly, the biggest source of noise for me is outside in the summer months when I leave the windows open.