Apparently there is no Priority baggage handling with AA flights within North America. Even if you fly First Class. Even if you are Emerald. You'd only get a tag only if the agent feels like tagging your bag Premium or when you are actually flying the Premium Class on transcon flights.

Within Europe, BA is quite lax in placing Priority tags on bags. Half the time I have to ask for it. Forget about IBERIA. I think the agents believe it as only 'for show' .

On Star Alliance flights too, within USA, UNITED does not place Priority tags for STAR GOLD members either. In Europe, not even STAR GOLD members get priority tags on Lufthansa flights even if you fly Business Class. Only Lufthansa-SENATOR members get the priority tags.

Within Australia, you'd get Priority tags as an Elite member of either Oneworld or Star alliances for Qantas and Ansett flights respectively.