It depends where I am going - if I am doing a trip to the EU I bring both my passports, as having my EU one lets me get through quicker, normally. I need to reenter Canada on my Canadian passport, so it comes too. Most countries the visa situation is the same for British and Canadian, so if it is a non EU country with no visa differences, I will just use my Canadian one. My passports are staggered, so that I should never be without one while the other is being renewed. It can also be helpful if I need to physically send off for a visa.