Adventure Bar Story!
Very very cool game, by the looks of it deeper than chaos rings 2 (though I wouldn't know as I haven't played them, but I have kept up with peoples impressions and comments...) I would seriously consider it my personal best RPG on the iPhone of all time, to this date.
Other than that I wanted to ask the same question as you to find similar games to this... lol
There's a game floating around called crimson heart, I don't have it though its very action focused from what I can tell and less RP... but again I haven't played it and the reviews while few are quite high. On second thoughts don't get CH... I just went to reinstall the free version because I deleted it and it said that my nickname already existed and I couldn't play on the network with it, except that it was my nickname that I CREATED MYSELF! ahhhhfhdhfh...
Funny, I have the opposite opinions on those games, but it's a matter of taste I guess.
Adventure Bar Story is a good game, don't get me wrong. It's just a little heavy on the "bar" side of things as far as coming up with items for your menu, etc. These things do help you level up, of course. It's deep as far as that's concerned. But not very traditional as far as a full-fledged RPG story goes and the combat system is a bit weak. Again, it's a very nice game for what it is. Just maybe not quite what I like in an RPG and, to be honest, hasn't really grabbed me yet. There's TONS of people who love it though so I wouldn't go by my opinion alone.
CrimsonHeart has actually been out quite a while, but I just picked it up (just got a 3GS and couldn't play it on my previous iPod Touch 2G). It's probably one of the best action RPGs on the app store and is very deep also in terms of creating new weapons, armor, etc. And unlike most action RPGs, it takes a lot more strategy to succeed -- not just hacking and slashing. That said, I find it to be also one of the hardest action RPGs as well.
Not too much comes to mind as far as the last six weeks, but if you haven't played Fantasy Chronicle, it's a fantastic turned-based RPG. Very polished and great story. (The other Kemco RPGs are good as well, just not quite as polished)