I rarely check a bag, but my experience has been uneven with UA, on which I'm a 1P. Of the times I checked a bag last year, it seemed like my priority-tagged bag came out among the first...but there was an occasion on a DEN-ORD flight (nonstop) that UA did not get my priority-tagged bag on the plane out from DEN on my early afternoon flight, or on any of the other flights going DEN-ORD that day. I think it finally came the following morning, but because UA didn't want to pay a courier to make a special run from ORD to downtown, the bag didn't arrive until after I had checked out of my hotel. After my meeting, I had to go back by the hotel to pick up my bag on the way back to the airport. Wasn't too happy about that.