Bigger isn't necessarily better when it comes to airlines.
American (AAL.O) and United (UAL.N), the two largest U.S. carriers, are also tops in customer complaints, a study released by the U.S. PIRG Education Fund on Thursday shows.
The consumer advocacy group found that the two carriers ranked in the top four for complaints for 2011 through 2013, based on Department of Transportation data.
The worst performer was Spirit Airlines (SAVE.O), which had the most complaints among 13 U.S. carriers each year in the study which spanned 2009 through 2013.
Southwest Airlines (LUV.N), the fourth largest U.S. carrier by traffic, had the lowest customer complaint scores for each of those years.
United Continental Holdings ranked second in complaints in 2011 and 2012, and dropped to third in 2013, the study shows. American Airlines was fourth in 2011, third in 2012, and fourth in 2013.
At United, complaints spiked in 2012 to 4.28 per 100,000 passengers, its highest in the five years studied, after technology changes during the merger with Continental caused outages and led to poorer service. United's complaint rate improved to 2.14 in 2013.
United spokeswoman Megan McCarthy said customer satisfaction has improved as the airline focused on enhancing service.
American, which merged with US Airways in December to form the world's biggest airline, stood out in terms of complaints about flight delays and cancellations, the study shows.
Spokesman Matt Miller said American, under new management headed by former US Airways Chief Executive Doug Parker, has improved in on-time performance and mishandled bags.
Delta Air Lines (DAL.N), the third-largest carrier behind American and United, improved its score from 1.96 complaints per 100,000 passengers in 2009 to 0.59 complaints in 2013. Delta has renovated airport terminals and expanded entertainment and food choices on planes since acquiring Northwest Airlines in 2008.
Delta "improved management and operating systems to help stay on time," said Laura Murray, consumer associate with the U.S. PIRG Education Fund. "It would be smart for other airlines to take a look at what it did."
Complaints about Spirit, which offers low base fares but charges for many other services, rose steadily each year, from 6.75 per 100,000 passengers in 2009 to 9.44 in 2013, according to the study.
Many of the complaints reflect "customers not fully understanding that we offer unbundled fares that let them control how much they spend," Spirit spokeswoman Maggie Espin-Christina said in a statement.
Complaints to the U.S. Department of Transportation about Spirit totaled just over 1,020 last year, out of more than 12 million travelers, she noted.
(Reporting by Karen Jacobs in Atlanta; Editing by Richard Chang)