Priority Tags usually make no difference. Why? Because in this day and age all luggage at major airports is scanned by the bar code they tie around your luggage.

The priority luggage tags are just a comfort for the premium passengers to think their luggage is being handled with mink gloves by semi-pro gymnasts when really its handled by the same monkeys as everyone elses.

Or in the case of British Airways, priority tags magically make your luggage come off last. Possibly because they fall in the way of the barcode and have to go to manual sorting.