If you surveyed travelers, I believe Delta would come out on top with the "worst" customer service. Their flight attendants can predictably be rude and with an attitude.
On Feb 10, 2012, I embarked on a trip from Atlanta to LA. The flight was grossly overbooked. In order to increase the number of no-shows and avoid payment, Delta changed gates from T2 to E18 just 10 minutes prior to boarding. This required running a marathon in order to make the flight. Elderly and handicapped folks obviously did not make the flight. Not only was this atrocious, I think it was also discriminatory and potentially illegal. However, this is clearly evidence that Delta is ruled by revenue management and don't give a rat's hynie about their customers.
Review about: Delta Airlines Flight.