Any bottleneck imposed by the PHII X6 won't be noticable in everyday gaming. You might get a little less bottleneck out of the PHII X4 980BE because it's faster and because games don't make use of 6 cores. But I wouldn't bother.
You don't mention the size PSU you have now, but upgrading to a HD 6950 will require a 500W+ PSU depending on what else you need to power. Use this PSU calculator to get a good idea of the size you need.http://www.thermaltake.outervision.com/
And don't forget to uninstall/reinstall the driver pkg with the change of cards.