Update: I think the audio content might be different. I just listened to the "Alice Cooper for President" version and there's some chatter at the end about forming a third party and mentions of some U.S. cities. I can't hear the UK version due to geographic restrictions, but it's highly unlikely those lines at the end are present.
This raises a new style question: Should I still use the same release group, or should I split them off?
EDIT: Here's a YouTube link. It may or may not work outside the USA.