Can't wait til it's released, I'm likely going to be getting it a day late from release, but it's still going to be an early birthday present from Kana, so it'll be worth it.
I've downloaded and played the demo, and can say they've improved a lot of things.
If I had to nitpick, I'd say I don't like the reskinning and recoloring of the menus, I think they had a good thing going with vanilla 13, and now they've made the colors a bit more...primary, I suppose.
I'd also say that the crystarium is more in-depth, but at first glance (without really being taught about it via tutorial or getting to play around with it too much) it's way more confusing than the original, but, again, this is due to lack of information.
Graphically, it seems to have improved, and they seem to have added a small black outline to the characters (much like what you'd see in Vesperia, or to a similar extent, Symphonia) which gives a bit more stylistic design and makes things look almost cel shaded, which is a good direction that many game developers have found for current graphical prowess (yes, Uncharted 3, I'm looking at you and your uncanny valley).
The addition of jumping any time is fun for the first 30 seconds, until you realize it's completely unnecessary in an RPG like this, and really only adds the need to push a button now, when you come to an obstacle.
Battle system is revamped, and seems to require you to switch paradigms a lot more often, but that could simply be because the demo is so early in game.
Weapon design is a give and take, Searh's bow/sword thing is the sexiest thing I've ever seen as far as weaponry goes, but Noel's weird sword combo thing (especially the way he weilds his secondary blade) just looks stupid, as well as the useless hilt on the larger blade, as well as Noel's costume design. The pants.,...just...no....he reminds me way too much of Sora, and not KH1 Sora, either.
The addition of Mog is inconsequential for me, but I'd wish they'd programmed more victory animations, so I don't have to see Serah hug him every minute and a half.
The end of the demo tricks you into thinking you're playing a lightning segment, but you're not, it's just a movie. Which made me mad.
One last thing to complain about is how Serah tilts as you turn her while running, way too steep way too soon.