There is a great blog-post about the improvement of Swift performance especially after the Swift 1.2 release.
The author ran several tests with different kind of code like Objc-like Swift code, Swift only and Objective-c only code. And the result was, that Swift 1.2 is much faster than before. He ran tests with JSON so it's a bit more practical than just algorithms.
Beside the 'real' performance, my personal experience about that is, that I'm developing much easier in Swift. I never liked the .h and .m files from Objective-C because it stopped the 'flow of programming'. Also I think the Syntax itself is much easier than in objective-c [with these brackets].
So I think, if you write a new Project from Scratch, Swift is much easier, faster and more elegant. (My opinion)