I always use my Canadian passport in the API. Always use my UK passport to enter the UK or the EU. One thing to remember to do is though you need to use your UK passport when leaving Schengen at passport control if you entered with it still show the Canadian one in the API when checking in bags at the desk. I wasn't thinking clearly once in HEL and handed the UK one in as my ID when I checked my bag to LHR with a couple of days layover in LHR. It must have then superseded the Canadian one in the API because when I did my OLCI for the LHR-YYZ leg it said a boarding pass couldn't be issued because I didn't have an ETA for Canada. Got it cleared up at the airport.