X and XIII were the only emotional FF's for me. I straight up cried during FFX, and the end of XIII got be teary-eyed but... the story in XIII is still nonsensical. The emotional part of it comes from the attachment to the characters, not necessarily the events that take place, or the overarching plot. For me VI's story stands alone in doing a narrative correctly, but even that has its faults.
My issues with XIII were that yeah, lack of information added upon no damn good reason for the group to be traveling together. They meet up so randomly, and just like that end up spending the entire game together. It happens in every FF, but I feel like in XIII their intentions were so muddy and obscure (to the point they were oblivious themselves) is a terrible reason for them to join up when compared to the other entries. They don't share anything in common (they do in being I'Cie, but not to the extent of) like with Avalanche, SEED, Yuna's guardians.
In terms of characters, I don't really think anyone connected with Snow or Vanille. They're so one-sided and really hard to relate to. It's just so odd to see such a "linear" (I have no issue with the linearity) game to be so all over the place with its narrative. Literally half the time I couldn't figure out where the hell I was, or where I was going (the goal), partially because the party was split up so much in the beginning and swapping back and forth.
The story was simple and pretty easy to follow. I don't think it's something that flew over my head or anything, I actually really liked Cocoon/Pulse. The blowing your mind comment confused me... not really sure what you were referring to, but the ending was essentially throw-away. Nice set up for a sequel I guess, but it came out of nowhere and was basically their way of saying, "oh we need to wrap things up."
It's still my favorite jRPG of the generation, but standing up for its story isn't something I'd put much effort into.