Well here is why I like FFXIIIs story (There will be a lot of spoilers in this post)

First I will touch on the overarching theme in FFXIII:
1. Minority vs Majority - Is it morally right to sacrifice a few in order to preserve the majority (The Purge/The world vs La'cie). Thinking about this from the opposite perspective, is it truly wrong to put others in danger to save the one you care most about? If so, then do you just give up on said person? (Vanille/Fang and Serah/Lightning/Snow)

2. Forgiveness - If one makes a mistake, what does it take to forgive said person, or for that person to obtain forgiveness. It is often said that the use of words such as "I'm sorry" is not adequate enough, but then what is? (Hope/Snow and Snow/Lightning/Serah)

There are more but these are the two main themes that pop out at me right now. (Trying to do this fast need to go to class soon. I apologize if my thoughts don't have a flow to them because I am rushing)

Now lets take a moment and consider the concept of Orphan. Orphan is basically the "god" of Cocoon and his one and only desire is to die and have Cocoon destroyed, in order to bring back the true god/goddess known as the Maker to have the world remade. To accomplish this, Orphan gives our heroes their powers, turns the entire world against them, and enslaves their loved ones in crystals. There is also the overlying threat that if the La'cie decide not to follow Orphan's plan, they will be transformed into thoughtless monsters. Orphan does all this just to make our heroes as strong as possible so that they can kill him. I find this story interesting because it literally reverses the usual heroes vs villain story line. Also, the main characters are being put through constant mental stress and moral conflicts. All of this is going on, and this only touches the surface of FFXIIIs story.

This is what Orphan says before you fight him, which pretty much sums it up:
"A haven, yea. Yet it must fall ere we be saved. Too frail a shell, and humans should not thrive. Too stout a shell and they would not die. Slaughter and salvation! Two irreconcilable Focuses we bore. Yet bound were we in a cocoon prison, impervious to our power. And so we thank you for granting us our longed-for birth. We are the Abandoned One, born but now to die. Our name is Orphan. By our hand, the world shall know redemption."

The music - Like all of its predecessors, Final Fantasy has always had outstanding music. I personally loved FFXIIIs music, although I agree that the battle theme got old sometimes :P. But as we all know, when there is any important moment FF always uses music that just makes the moment, FFXIII held up to this standard. Here are a few examples:

Oerba - http://www.youtube.com/watch?v=GLa0N7kVlfo
Nascent Requiem - http://www.youtube.com/watch?v=R-jpwEd4KSY
Born Anew - http://www.youtube.com/watch?v=0qyavbSmxW4 (read the translation in the comments. Simple but powerful)
FFXIII Main Theme - http://www.youtube.com/watch?v=CxSXm8qGjS8 (Has a few names, the wish, the promise, has many different variations used throughout the game)
Barthandelus Theme - http://www.youtube.com/watch?v=vbMbQLUr9cA (Everyone hated this villain, but i thought he was awesome. Every time he spoke I got chills.)