Originally Posted by
atsak
I present the passport of the country I'm travelling to to the check in agent (in my case Australia) if needed. Upon leaving Australia, I have to present both passports at check in to confirm no visa requirement to Canada but my Australian at emigration so they can check me out. It's not a big deal. I travel on my Canadian anywhere else though, since it matches my accent (though not my birthplace)!
Actually, no. Like Bartolo says, use your Canadian passport when chicking in with AC, both ways. Just use an EU passport when going through passport control in and out of the EU.
Even if going to a country the requires Canadians to have a visa, I leave my Canadian passport in the file, but when the agent checks for entry eligibility at destination, I show the second passport. Which actually is not entered in the file, I believe.