Aeris' death is pretty much iconic at this point; that's the difference, in my eyes. It's a part of popular video game culture. It's not just a surprising turn of events in some random game, it's a defining moment of a defining installment of a defining series of games. I mean, seriously. It's not my favorite FF, but VII was probably more popular over a wider market than any other installment before or since. That's why the plot is so well known at this point. VII was huge. Ffs, I traded in my N64 and bought a Playstation just to play it.
There's no such iconic moment in VI, even though I think it's a better game. The difference is that VI was never as popular as VII at its height, so the story never wormed its way into the public consciousness the same way.
Tl;dr - Not all spoilers are created equal.