Aerith's death scene did not feature the Final Fantasy "Prelude," but "Aerith's Theme" - which isn't a piano piece, but does include a piano in parts, among the orchestra. The style is somewhat similar in places to the new intro music.
Great call on Square's part to leave her theme playing during the subsequent battle - switching over to the boss theme would have killed the mood completely. Instead, like many people, when I fought Jenova-Life for the first time, I was glaring at my TV, determined to avenge her. One of the greatest moments in gaming, if not THE greatest.