Apple says the A6 chip inside the iPhone 5 provides up to two times the performance of the iPhone 4S. Not only do benchmark results prove that out, the iPhone 5 is faster than the fastest Android phones in the U.S. right now. As you can see from the above results, the iPhone 5 soundly beat the Galaxy S III and the HTC One X in three separate tests that run on both iOS 6 and Android: Geekbench 2, Linpack and Passmark.
In everyday use, the iPhone 5 proved snappier than the S III and slightly more responsive than the One X. Upcoming quad-core phones like the LG Optimus G and Galaxy Note II should make this a closer contest, but in general I've found skins on top of Android to add lag. It might take a quad-core Nexus phone running pure Jelly Bean to truly rival the iPhone 5's sheer speed.