Ok, this is definitely a bug in Xcode 5.0.1.
This is confirmed by Jason Molenda on Apple Developer Forum. The only workaround for now is to use older version of Xcode and the older version of Mac OS X because Xcode 5 requires OS X 10.8.4.
There is no announced ETA for a fix for this issue. Direct question about ETA on Apple Developer Forum is left without answer.
UPDATE 06-Nov-2013:
Today a pre-release version of Xcode 5.0.2 became available on developer.apple.com. This version fixes (among other things) the following issue:
Debugging an application on a device running iOS 6.x causes the application to crash with EXC_BAD_ACCESS. This has been resolved. (15310896)
I have installed the new version and the issue is indeed gone. Now I am able to debug apps on my 6.x devices again.
Jason Molenda in thread on Apple Developer Forum said:
I'm told you can submit apps to the app store with this Xcode 5.0.2 seed.