Swift is claimed by Apple to be faster than Objective-C, and as you said it is faster in those sorting algorithms, but for the usage of iOS development, a simple user would not recognize the difference between an app developed in Swift or Objective-C. I developed a lot of apps in Objective-C that are in apple store, and now several in Swift and so far users can not tell the difference if one is much faster than the other.
Swift is unlikely to result in applications that run much faster than applications developed in Objective-C. Even though the two languages are quit different, both target the same Cocoa and Cocoa Touch APIs, iOS and OS X a, both are statically typed languages and both use the same LLVM compiler, so they are not that different after all. There will be performance differences, as the two languages aren’t identical after all, but don’t expect significant differences.
Swift is also developed from Apple to appeal to new programmers because it is similar to languages such as Ruby and Python than it is Objective-C.