According to a report on GamesRadar sister site, Edge Online, the PS4 is up to 50% faster than the Xbox One. Although the hardware is roughly the same in terms of power, it seems Sony's machine makes better use of the technology. One source told Edge that memory reads are 40-50% faster in PS4, and the ALU (Arithmetic Logic Unit) is 50% faster.
What does this all mean? The article gives an example. Without optimisation for specific console, a multiplatform game could run at around 30 FPS (frames per second) at a resolution of 1920 x 1080 on PS4, compared to 20 FPS and 1600 x 900 on Xbox One. That's a significant performance difference, and one source describes visuals on Xbox One as "horrible".
According to the anonymous sources, Microsoft has recently increased the clock speed of Xbox One to 1.75Ghz (from 1.6Ghz) but this doesn't offer a significant boost to performance. Both Sony and Microsoft are making hardware improvements right up to launch, with graphics drivers being one of the main areas of improvement. However, Xbox One has been slow to upgrade, according to the article.
PS4 launches in the US on 15 November, and 29 November in the UK. Xbox One launches worldwide on 22 November.