That's a tough one. Lately, I also have been enjoying Shadow Sun, which I think is underrated, as well as 9th Dawn and Doom & Destiny.
I know some people put down the Kemco games, but I still count Fantasy Chronicle amongst my favorite turn-based iOS RPGs. And Stone of Life is a favorite KRPG.
Then there's The World Ends With You, Final Fantasy Dimensions and the Chaos Rings games. KOTOR for Star Wars buffs. And PeteOzzy reminded me of one of my big favorites -- Bastion. Oceanhorn too if you include more Zelda-esque RPG/adventure games.
I'm glad I'm not the only one who finds this to be a very tough decision. 9th Dawn, Avernum, Baldur's Gate, Bastion, Dungelot, Dungeon Plunder, Isle of Bxnes, King of Dragon Pass and countless others really deserve mentions but if I were to choose just one?
The World Ends With You.
But yeah, there are so many deserving to take its' place. I'm spoilt for RPGs on iOS!
Edit: I maybe forgot KOTOR, I think that may replace TWEWY...
Skill-based combat with a strong RPG progression elements and a full on story backed up by 2 books, Infinity Blade series would have to be my favorite on iOS.
My other favorite RPGs on iOS are the ff:
Chaos Rings series
Doom & Destiny
Symphony of the Origin
Slayin (even though it has only minor RPG elements)
Heroes of Loot (as with Slayin)
Heroes & Castles (as with Slayin)
Exact-Psience My 2014 Top 10 Games of the Year: Monster Hunter Freedom Unite, Hearthstone, VVVVVV, Battleheart Legacy, Wayward Souls, Bug Heroes 2, Powerpuff Girls Defenders of Townsville, Deep Loot, Monument Valley, Bioshock Honorable Mentions: Traps N Gemstones, Bardbarian, Goblin Sword