I don't know about the gameplay being judged as too complex, but I can confirm that a ton of story was cut out.

Final Fantasy IV DS Interview | GameBrink.Com

I've heard elsewhere that there may have been a time-based event for rescuing Rosa they originally had planned where if you didn't rescue Rosa by the time the timer ran out, you got a game over.

I haven't read the interview in a while, but I think it said that the Lunar Trials were a mish-mash of bits of what they wanted to add to the story but couldn't the first time around.

I'd like to see some of the subtle parts of the game made clearer, since it seems like a lot of people don't catch really amazing character traits or bits of storyline unless it's shoved right in their faces.

There's closer tabs kept on the game on the GameFAQs board, and a lot is being uncovered through th developer's blog and the Famitsu scans.

-You can view the thoughts of your characters while in town through the menu.
-A skill system where when a character is going to leave your party for good, they give you an item that will let you adopt their skill or skills.
-The skill system applies to NPCs too, which may give you other skills when you reach certain points.
-A couple big game news site reports claim that there will be combos similar to the dual techs from the Chrono games, but that hasn't been stated in any Famitsu pages or the dev blog.
-They're adding some new creature called a Poochika that you can assign skills and change their face a bit, and it can be used in battle.
-The Namingway has been changed. It no longer renames characters, and it has at least two new functions. They appear to be Mappingway and Dubbingway, whatever the second one means.
-The people in charge say there will be a feature that adds replay value to the game, but isn't like a New Game Plus.
-New minigames.
-Some skills are getting altered, like Dark has been altered into a buff move that sacrifices defense to improve offense.
-The boss battles, and maybe the regular monster battles, are being tweaked to add new challenge to the game for the hardcore FF4 fans that have played the game enough to have memorized how to beat them through repeated replays.
-And the obvious: voice acting, FMVs, and cutscenes.


There's also some speculation over at GameFAQs that they may add one more character to the playable roster based on the way the Character area is set up on the official site. Four portraits in the back with three spaces remaining on the vertical bar on the right.