I realize I'm probably the only one here who cares but the game arrived in the mail today and I spent a bunch of time playing.
It is two games in one, and in fact they were separate releases in Japan. I spent most of my time in Puzzle & Dragons Z which was the first one that came out in Japan. The puzzle gameplay is the regular P&D stuff but they added some Pokemon-like RPG story things to keep it interesting. So far the story is kinda dumb but its amusing enough and breaks up the puzzle stuff nicely. If it was just straight up mobile game to 3DS it would kinda suck so its nice that its there. Do a bad guy has broken up the world into puzzle pieces and so you set out to find...yes, World Piece. Well, pieces since you need more than one to bring everything back together.
The Mario side of things is not story based at all. Peach is kidnapped, Mario goes to save her. Thats it, go. Difference is the overworld looks like the NSMB level select and you do all your creature evolving in Toad Houses. All the monsters are Mario enemies.
Though speaking of creature evolving, each game handles that stuff a little differently. In Z you get monster eggs which you have to decide to hatch to get the monster, or to use it to level up one of your existing creatures. In Mario "eggs" hatch automatically into whatever monster, which you can then feed to one of your other monsters to give it the XP. Its a subtle difference but it means in Mario you can level up a creature and decide later to use it to improve your other creatures, but Z you have to decide which way you want to use it from the start.
So yeah anyway long story short is they are different enough to be each be worth playing, and there is a lot to play in each of them so if you like puzzle games this is worth checking out. Also it looks SOOOOOO much better than the mobile game. The monsters all animate and have 3D effects rather than just being still images in the mobile version. They are really polished.