Quote from Shanghai;1208549:
GBA4iOS, if you're itching for some GBA emulator that's the best right now. No jailbreak required either. You need iOS 7 though.
I refuse to update my iOS to 7. Forever version 6.1.3!
Jokes aside, I'm pretty knowledgeable with Japanese iOS apps, since I'm into a lot of them.
Fast paced... If rhythm games fit that category, "Love Live -- School Idol Festival" might be good for you. They were boasting 2 million players worldwide, which is probably more than Puzzles and Dragons.
LineZeta was another I enjoyed, but it kinda sucked after you received a UR [S]gundam[/S] robot, and it was weak as hell.
On the other hand, you might like some of the tap-adventure games like Mosaic (paid) Lost City (free, IIRC) by FireMapleGames. Stunning graphics and great music, but it's a little too easy. The pro of this is that you can still get them on an English iTunes store.
To be perfectly honest, the iOS doesn't really have fun games. The android is where you have the best of them.
At least for the Japanese iTunes store, most of the games involve the "Collecting Card" games where you literally spend thousands of dollars for UR/SR cards which will give you an advantage over other players in events. Not worth it.
EDIT: Danmaku Unlimited is a great game. It's the curtain fire shooting, and it's really similar to Touhou. The con is that it's also way too fucking easy (Normal or Easy is a joke), and it costs $0.99 for the full version (lite version available)... I haven't tried the second one, but I assume it'll be similar.