I like it better than Final Fantasy III DS simply because I couldn't stand how unforgivingly tedious every random encounter was in that game. They aren't really comparable, though, since they're a totally different kind of game.
The battle system is totally real-time strategy--you have leader units, which are normally story characters: Vaan, Penelo,
(SPOILER)Ba'Gamnon, temporarily, etc. Each of these leaders has a few minions under their control for a total of normally around 15-20 units you're controlling on each map. Like any other real-time strategy game, you eventually gain means to create your own new minions for your leaders up to a certain unit count, should you lose some over the course of the map.
The minions that you can choose from are set up prior to the battle, and you unlock new ones through a system not unlike a miniature version of Final Fantasy X's sphere grid. They are the usual Final Fantasy critters you'd expect... Chocobos, Bombs, Sabotenders, etc. All sorted into elemental categories. You can choose a total of five types of minions to bring into battle, among three tiers of overall stats. As you encounter and defeat espers throughout the story, their nodes will become available on this grid as well.
The units move pretty slow on the map, but overall the game is pretty well paced. The movement speed is just about right to give you time to nicely micro-manage your leader units to cast the correct spells and abilities during a fight.
Speaking of skills and abilities, the idea of "gambits" have been implemented, but in an extremely simplified version...basically you can select one of your skills for each leader unit, and he/she will perform this skill by default if it's ready to be used. Other skills must be manually selected and executed.
There is no "dungeon-crawling" per se, just individual maps for each level.
Like I said, the gameplay is fun yet simplistic. I would think that it would be generally accessible for anyone.
I can't understand enough of the game to know the details of the story, however I understand the underlying concepts of what's going on and while I won't spoil anything (there isn't really that much to spoil) I will say that so far it's very light...Seems like light humor has taken the center stage in this one. Don't expect the same kind of big-picture story arcs as you got in Final Fantasy XII, it's wholly different.