Impressions about the demo:
Graphics - Really nice, the game feels 3D and 2D/hand-drawn at the same time, the monsters in battle are especially great to look at. It's a bummer there are no real fight choreographies, just the old "guys-slashing-the-air-to-hit" thing. The 3D effect is also implemented in a very effective way, as far as I'm concerned. I love the way the city looks, with the subtle switching between planes, while still looking bidimensional, it's also very unique as far as cities go. That's something that goes for the whole game, there's a unique art style, unlike any other game, so BD doesn't feel as the same generic RPG, at least in the visual department.
Sound - Good but nothing revolutionary. The main theme is nice.
Dungeons - Not much to say here, they're not something special, but at least they try not to be straight corridors; I love the uncharted hidden passages, every RPG should have them. I like the fact certain job abilities (Freelancer) influence the way you interact with the dungeons as well. I'm glad there are visible bosses and savepoints right before them: no use in being taken by surprise by an unavoidable boss after a cutscene or having to grind your way to the boss after you die.
World Map - There is one. Seriously though, just the same old world map, it's just that so many RPGs tried to do away with it, it's good to see it again. The random encounters are still there, I've never been much bothered by them, but it's wonderful having the ability to actually decide how many encounters you want: the fact you can just turn them off from the options is a revolutionary idea.
Job System - Dare I say, one of the better structured I've ever seen? Even just the few jobs available in the demo are diverse enough, but there's gonna be much more if those ??? are any indication. I also guess you can go well over the 3rd job level in the full game. The way you can combine active and passive abilities from the job you have and the ones you've mastered, offers huge customization possibilities for your party.
Shops - It's nice to have the chance to swap the new items for the old ones on the fly, without leaving the shop, the letters ranking the compatibility of said weapons with your current job are also a cool addition. The traveller shop, gradually unlocked via street pass and villagers is also a neat idea; I imagine that through it you could possibly be getting rarer and more powerful stuff early in the game, assuming you put enough time in it.
Battle - Wow, it's been long since I truly had to make clever strategic decisions to defeat even average goons. When I kicked that minotaur/dragon's ass it felt great, and it felt as a real accomplishment, as if my strategy paid off. The original brave/default system works wonders, at first it's just 4x brave 4x attack, but going on you understand it's much more complicated than that, especially in regards to the default option, which is underestimated at first, but becomes your most useful asset in battle. Moreover you can simply adjust the difficulty on the spot, that makes things comfortable for everyone.
Plot - Now, I hope (and I'm positive) that this was just due to the demo's limits... but the plot is nonexistant, as well as the characters. The fetch quests were horrid, the ones where you have to kill a boss were the minimum you expect from an RPG: ordinary stuff. I know it's a demo, so they didn't want to bog down the package with endless screens of text and numerous cutscenes, instead preferring to show the awesome gameplay, but they could have at least shown a brief recap of what the whole game is about, the demo felt totally aimless in that regard.
All in all it's been pleasurable playing through the demo, I think I'll buy the game, even though right now it's not a priority; I appreciate the effort they put in what is, in the end, just a demo, but I can't shake the feeling they made it too self-contained for its owm good, as if it was a game on its own, it doesn't offer enough gleams about the rest of the game.