When programming a CPU intensive or GPU intensive application on the iPhone or other portable hardware, you have to make wise algorithmic decisions to make your code fast.>
It's very hard to collect "hard data" for this that's not misguiding.
The biggest problem with doing a feature-to-feature comparison like you suggest is that the two languages encourage very different coding styles. Objective-C is a dynamic language with duck typing, where typical C++ usage is static. The same object-oriented architecture problem would likely have very different ideal solutions using C++ or Objective-C.
My feeling (as I have programmed much in both languages, mostly on huge projects): To maximize Objective-C performance, it has to be written very close to C. Whereas with C++, it's possible to make much more use of the language without any performance penalty compared to C.
Which one is better? I don't know. For pure performance, C++ will always have the edge. But the OOP style of Objective-C definitely has its merits. I definitely think it is easier to keep a sane architecture with it.