Well, as far as surface level stuff, the presentation just feels very reminiscent of Golden Sun to me. The battle screen and the overworld are laid out in a very similar manner to Golden Sun, and since that's primarily what makes up the demo, it's something I can't help but notice.
But even in terms of enemy encounters, the Brave/Default system adds a fluidity to the combat that reminds me of the djinn system in Golden Sun. In a lot of RPGs, combat is pretty standard and rigid. Your characters make progress over the course of the game, but individual battles are pretty predictable—your characters are capable of specific things throughout the battle. But the Brave/Default system is sort of like the djinn system in that is changes what your characters are capable of from turn to turn. In Golden Sun, the state of the djinn you have set to your characters determines what kinds of abilities and summons that character is capable of in that moment. Similarly, characters in Bravely Default have certain abilities available to them when they keep their BP (Brave Points?) above 0, which you can build up through passive abilities or by waiting through a turn by Defaulting (defending, essentially). It makes each turn feel a lot more dynamic than most other turn-based RPGs.
Obviously it isn't exactly the same—there doesn't seem to be any out of battle puzzle solving that GS is famous for, and the jobs system in Bravely Default is where most of the variety comes from rather than djinn collecting, but there's definitely some similar vibes here.
Then there's stuff that's totally different that's still really cool, like the equipping system. You can give characters two weapons, allowing them to attack with both in a turn, or swap one out for a shield to increase defense and evasiveness, or leave one hand entirely empty if the character in question has an ability that benefits from that, etc. And every piece of weaponry or armor that you equip to each character can have a different effect on their stats depending on what kind of class they are. Sometimes equipping two weapons brings their overall damage potential lower than if they simply had one.
Basically, it's a micro manager's dream.