It really shouldn't be running applications any slower, at least not perceivably (you may be able to tease out slight variations in benchmarks for example)
I know it's benchmarks, I'm just using it as an example of why Windows 8 doesn't beat Windows 7 hands down and why all it is is basicly a new interface, with the odd tweak here and there. It's perceived quickness is mainly down to:
1. lack of aero (good or bad, make up your own mind. I'm not too bothered about aero so this could be seen as a good thing. Turn off Aero in Windows 7 and you'll see it also speeds up.)
2. It cheats (turning off the screen quite a while before actually shutting down for example)
So all I'm saying, posters who say that it is "much quicker than 7" are either easily fooled or lying through their teeth. All Windows 8 is, is a different interface and maybe a couple of small tools added on as well.
And for the record I have it on my laptop, and although it's fine, once you sort out the issues that crop up with updating to it, I can't really say it was worth the hassle or will be worth the full upgrade price once the £25 offer finishes. That said, you may as well buy a full copy for a new PC as the interface can be swapped with Classic Shell or similar tools, should you need to swap it (though the Start Screen and Desktop between them are fine) and it is the newest Microsoft OS.
This basicly sums up my previous points from this thread so I'm done.