As of now, it's tChess Pro version 1.7.1. I've been using it on the iPhone for almost three years: the interface is easy and intuitive, the features are nice, and the playing engine is reasonably strong. (I lost the first game I played against it, and many more since then.) There may be stronger engines, but tChess is snappy!
There's a dual core option on the iPad 2: not sure how many ELO this would add. But if you're looking for raw strength, the iPhone and iPad are the wrong platforms.
Most of these screenshots are from my iPad, with the exception of one iPad screenshot grabbed from the developer's website. But the iPhone look and feel is very similar: I don't feel all thumbs with this GUI even on a tiny screen (compare my ChessBase 1.1 hatefest, which was essentially a rant about ChessBase's GUI.)
I'm about to start a new game.
Grr...only a draw. (Trust me, I wasn't going to show you a screenshot with my usual rating of 1650.) And tChess was not set to play at full strength.
I can find out that the game was a Marshall Attack, ECO code C89.
Perhaps I should look at a Fischer game instead. Or I could look at the game that one of my Industrial League teammates just sent to me. Or I could open a database of my own games. Or I could play through the tournament game I just played on my iPhone, identify my gross tactical blunders, and email the game score to myself. (My biggest complaint: tChess Pro does not support any variations within PGN. It really should.)
You can have up to 25 PGN files on the device: before I started this review, I had twenty on my iPhone. One can copy and paste PGN into tChess, and perform some basic editing on PGN headers. Even the ChessBase of twenty years ago had far more advanced database features, but the ease of accessing the game you've forgotten is a delight.
Frustrated by your ratings history? Delete and create a new player profile.
This app is well worth $7.99!