The Xbox One S is not only smaller, lighter and more efficient than the Xbox One, but the company has taken advantage of the use of an improved silicon (less lithography) to improve performance. The new graphics processor from AMD has been Overclocked @914MHz making performance pass the 1.31 to 1.40 TFLOPs. The new GPU is coupled with an increased width ESRAM, enough to throw bandwidth from 204 to 219 GB / s.
Xbox One S Vs Xbox One Performance Test
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If we add the two improvements, the Xbox One S is 6.1 percent faster than the Xbox One, but depending on the game there is an improvement of up to 8.1. The folks over at Digital Foundry have tested the new console, and except castrated games at 30 FPS (where there is no improvement), in other games from the above video you can see striking improvements, especially in Project Cars (up to 11 percent playing). Although obviously, despite this performance the improvement is still several steps behind the PlayStation 4, but any improvement is grateful for those who are willing to buy it.