Depends, IMO, on what kind of riding you think you'll be doing more of- fixed or geared. If you're going to do more fixed riding, convert the frame you like most. If geared, keep the frame you like most as it is and convert the other. If you're not sure you'll like fixed riding, don't remove any braze-ons just yet.

I'd put the Campagnolo on the bike I planned to ride more often. I'd also lean toward converting the bike that has the tighter clearance between the rear tire and seat tube.