Okay, well before I answer the easy question, let me help you by knocking FFVI off it's pedestal a little bit so you can feel better about appreciating it for what it is and not what other people feel it is.

Whatever game is currently your favorite FF right now, I am 99% positive it will still be your favorite FF after you play this game, and you will most likely still tout is as the superior to this old classic. So if VI doesn't blow you away and becomes an instant favorite for you, it's okay.

VI did a lot of things for FF and the genre back in 94. You will most likely not notice it, because it's mostly things that are common place in the genre afterwards and is largely taken for granted. Even if you understand the game's historical significance, it is not quite the same as experiencing at the time, so understand the fans are kind of bias in that way and it's no fault of yours if you don't feel it was as magical as say *insert FF title you like better* when doing something similar.

This is not to say that you cannot hope to have the same experience and love for this game as other VI fans, I'm just going to say that it's highly unlikely VI is going to usurp any of your own feelings about the best games in the series that you may possess. At best you may simply enjoy the game and in all honesty, that's all I hope for anyone who plays this game for the first time.

As for your main question, yes the Anthology Version is mostly a port of the SNES version with a few of the item names corrected (Biggs instead of Vicks) but most of the game is the same, though Anthology adds a cool CGI opening and ending, and has a collector's section that gives you a bestiary, music box, and a few other fun goodies you can access.