Hello Paul. Since your post, ATI have released new drivers. 10.7 is the latest one to date. If you don't have it then I'd recommend installing that. But first remove your old drivers before installing the new ones to avoid errors. I have both the games and i can say that I've never had those issues.
I do have Windows 7 32bit and the games run fine so we know its not that. Your GPU fine to run them both and your RAM is more than enough. I think it's a software problem. I maybe wrong but have you tried re - installing the games? If you have and the problem persists consider looking to see if you have a program running that maybe causing the issue.
If that still doesn't work then download 'Defraggler' (free) and defrag your game files not the whole hard drive. If you have the games on Steam then you can right click them and select properties and then Local files and then select Verify integrity of game cache and if that doesn't work then i don't really have anything else to suggest.