I've often wondered about this, too. When I emigrated to Australia in 1994, I entered on my U.K. passport, with the residency visa in it. During the time I was there, this U.K. passport expired, and I got a new one from the British Embassy in Canberra. I also took citizenship and got an Australian passport. However, when I went through security to leave Australia at BNE, when I handed over my Australian passport, the guy looked at it, checked something on his screen, and handed it back asking "do you have an alternative passport?" Whereupon I handed over my new U.K. passport (no visa in it, remember), which seemed to satisfy him. Was this solely down to the Aussie passport not having a U.K. entry visa in it?

It spoilt my day a little, as, up to that point, I had felt a bit like James Bond, carrying two passports in secret.