There are sometimes Driver versions that cant run games at certain settings and resolutions or perhaps becasue there not fully compatible with the games engine yet. Also it may be an issue with the 64bit drivers themselves.
Look at the Release nots of 6.5 and it may tell you some issues with the games you are having issues with
Look here :
The following section provides a summary of open issues in the latest version of Catalyst® for Windows XP Professional x64 Edition. These include:
Using Movie Maker 2.1 to capture video under Windows XP Professional x64 Edition results in the captured video being corrupt. Further details can be found in topic number 737-19820
Attempting to re-enable any display device other than the primary or secondary display device that has been disabled by CrossFire, may result in the operating system failing to respond. Further details can be found in topic number 737-21663
161550 The 720p50 and 1080i25 checkboxes are not added in the Catalyst Control Center by default when connecting a single CRT (PAL support) under the Windows XP Professional x64 Edition operating system. Further details can be found in topic number
165188 Disabling 50Hz timing support through the registry may result in the Windows XP Professional x64 Edition operating system entering a continual reboot. Further details can be found in topic number
ATI Customer Care
However apparently there should be know issues...Then again they may not know of it. I would update or reinstall your current drivers but you must do the following :
Installing Graphic card driver efficiently!!! When you Update your graphics cards drivers theres ways that you should go about it. Follow these simple steps below.
1.Download and install ''Driver Cleaner'' Here:
2.Uninstall your Current Display drivers such as your ''ATI'' or ''Nvidia'' drivers.
3.Now run ''Driver cleaner'' and depending on the Drivers you have you will have to select either ''ATI'' or ''Nvidia'' from the drop down menu. Only select the main title of the driver in the drop down such as just ''ATI'' or ''Nvidia''
4.Once you have selected Your driver click on the ''Start'' button and this will now start the driver cleaning process. ( Do this twice to be sure )
5.Now reboot your system and Download the latest Nvidia or ATI and go ahead and install them.
Doing this avoids driver corruption and conflicts so you can now enjoy smooth gameplay.