I finally watched it for the first time recently.
I did see the remake before and while I didn't really hate it, I can't really remember anything about it other than that ridiculous backstory with Billy And Agnus.
One of the nice surprises for me was how funny the movie was. Margot Kidder and the woman who played the Housemother were fun to watch.
I've seen some of the clips that made the movie a classic and was worried I would be disappointed when they came up, but I didn't. The famous eyeball scene got me anyway.
I'm in agreement that this movie works because there is still a mystery about Billy even at the end. The fact that it's just some random psycho makes it very scary.
It's definitely near the top of my favorite horror films list.