Now that we're down to the nitty gritty, this is actually pretty tough. I like every Psycho movie except the remake and I feel like there was little to no drop in quality save for a few hiccups in Psycho III. On the other hand, as much as I like Friday the 13th, you can easily argue that Parts III, V (although again, I love it), VIII, Jason Goes to Hell and Jason X all have some major flaws.
However, this competition is about franchises, and when I think of them, Friday the 13th is the one that sticks out more in my mind. I'm voting Friday the 13th by the slimmest of margins, while also saying that I think I prefer the Psycho franchise from a personal standpoint.