I had the same experience as OP, although I played it before I knew that so many people were ZOMG FF6 IS THE BEST GAME EVAR KEFKA IS TEH AWESOMESAUCE! I though it was a decent game and I enjoyed it, but I didn't see anything special in it. Many years later I played Chrono Trigger on an emulator after hearing a lot of people say how brilliant it was and I wasn't disappointed.
I think one of the most important things to remember is that it was one of the first games to have such an emphasis on storyline and characterisation, so it seemed amazing when it came out because no other game was like it.
Or, to put it another way, it was a big fish in a small pond.
Also, there are a number of reasons relating to internet fandom (and fandom in general) which mean that the game will get more praise from its devoted following than it would have if it had been released in different circumstances.
