After having replayed those levels for the LP (and having quickly played with the NA demo which uses the J demo's layout), I can state that the demo is just slightly above Normal difficulty. And part of that could be that they took the first and last level from the first dream sequence (there's 2 levels between them that gradually introduce you to some neat tricks, gradually spike the difficulty curve, and let you get used to the game mechanics before throwing a true challenge your way).
The demo goes from the cakewalk level to the OH GOD, WHAT IS THAT THING CHASING ME OH FUCK level in mere seconds.
I'm also enjoying the full game a lot more than the demo, since they cut A LOT of the cool stuff you can do from it. Checking out the bar, seeing some of the non-boss levels, and hanging around the landings adds a bit of fun value to it while breaking up the gameplay. They also did a sort of cut down version of the first day's events. There's a couple bits there they removed. Probably to speed you along.
Also, some of this could be that I was playing a game in my non native language at 4 am while recording myself. Which also lead to me not using an important game mechanic. Boy, was my face red.