Upon reflection, I think the first time I saw Citizen Kane I was young enough not to be aware of the "twist" or conscious of its position in cinema history. I remember finding the increasing melancholy in the film strange and almost discomforting, because it wasn't the sort of narrative arc I grew up being exposed to, and being moved to tears a lot.
Even if there isn't a twist, in the film itself or built into its original marketing like with Psycho, it's a very cool experience to be with someone seeing a major cultural touchstone for the first time, or even something that's been forgotten and maybe wasn't groundbreaking, but because it wasn't, everyone isn't familiar with it via cultural osmosis.
Oh, I saw Metropolis with a live orchestra a number of years ago and knew nothing about it going in, which I think made it a better experience and more open to my finding meaning within it than if I had been aware of the political leanings of the screenplay's writer beforehand.
A Meat, go watch M.