The feel, for me, is from the combination of Sakaguchi's game direction, Uematsu's music, and Amano's art direction. It has less to do with individual components of the game and more with the feeling imbued by their careful attention to detail in creating the world. Even though the games are made by teams it's obvious how strong their influences were and I believe their departures are why so much of the magic has been lost in recent titles.