Yeah, I guess it sounds most likely to be something software related. If the crash dump doesn't help, then I guess the next option I'd try is to google search "farcry 3 bsod" and "metro bsod" and try out all the crazy solutions people mention using to fix their BSODs. Sometimes the solutions can be really weird stuff when it's a software issue. Still, I always thought that the ONLY time a BSOD will occur on modern Windows is if it is bad hardware, bad drivers, or a corrupted OS install.
Hmm... in that case, it might be worth trying a scan on the OS files "sfc /scannow" http://www.howtogeek.com/howto/windows-vista/verify-the-integrity-of-windows-vista-system-files/
Still based on what you are saying, I kind of agree it might be driver related. Maybe the driver sweeper didn't clean up properly. You might try this:
1. If you used driver sweeper on the catalyst drivers, then reinstall the same catalyst drivers and then run the regular uninstaller on the drivers without using driver sweeper... Then install the catalyst drivers again and try the game.
As for hardware, I wonder if it could be power... the R9 290 does consume more than both the GTX670 and 7970 under certain conditions (although not a lot more than the 7970).
BTW, I'm curious, what brand&model did you get? (this is unrelated to your problems; I'm interested in one of the Asus R9 models.)