About as fast as an Atom
To put it in perspective that puts it about level with an Intel Atom x5-Z8550
I.e. you're not going to get a good experience running Photoshop on it as in Microsoft's demo
Even worse consider SIMD. Intel pointedly reminded everyone that recent SSE instructions are still patented here
Now it's fair to assume that Photoshop uses a lot of recent SSE which could be translated to ARM SIMD. However the Intel blog posts is essentially threatening the OEMs with a lawsuit if this is enabled. The best way to avoid that is to disable SSE to ARM SIMD translations but that has a significant performance impact. I.e. not only would you be running Photoshop on a processor equivalent to an Atom, it's won't implement any SIMD instructions. And there's the question of how many Win32 x86 applications actually require SSE since it has been around for long and is actually a pretty well designed SIMD instruction set.
It's shame really. I'd love to see a Win32 phone based on Atom or Snapdragon chips that let you run Win32 applications. In fact that's what I thought they'd do with Windows Phone and/or WIndows RT. Unfortunately they decided to disable non Microsoft WIn32 ARM executables to try to get people to use Metro apps from the store. Now Windows Phone is dead could they try WIn32 Phone? On an Atom I reckon that might be viable. Most of the Android apps I use have a Win32 version. Chrome and Opera do. Pleco, my favourite Chinese dictionary actually run well on Windows Mobile before it run on Android and iOS. Problem is killing off Win32 WIndows Mobile applications on Windows Phone has alienated a lot of ISVs. Even if Microsoft launched Win32 Phone now, it's not clear if they'd bother to support it given how dominant Android and iOS are.
I suspect the ship has sailed. Everyone has moved on to Android and iOS and another phone OS isn't really viable.