Is the head badge riveted or just stuck on?
If it's riveted on, I'd remove the headset and cups from the bike with the badge, then use a half round file to file off the rivet heads on the inside of the head tube. I'd then file the back of the badge flush and use a strong double sided tape or perhaps epoxy to stick it on the other frame. If it's just stuck on, you'll have to tray and pry it off carefully.