It's not the first time airlines and booking sites have had a spat over listings—American pulled listings from Orbitz and Expedia in late 2010, reinstating them in 2011 after reaching a new contract with Expedia, and as part of an Illinois court ruling in the case of Orbitz. And it probably won't be the last dispute as airlines look to gain revenue, said Ed Perkins, contributing editor for SmarterTravel.com.
"It costs the airlines a lot less to sell a seat directly on their own website," he said.
Increasingly, it's a smart bet to compare using one or two aggregators such as Kayak.com, Momondo.com or Hipmunk.com, which pull their results from across hundreds of sites. Booking sites make their own contracts with airlines, which mean prices and partners vary from site to site, said Andrew Young, editorial director for Travelzoo. Often, carriers keep their best prices for their own sites. A few—notably, Southwest—only list fares on their own website. "No one site really covers all the airlines, so you have to shop around a bit," he said.
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Check the airline's site separately, anyway, making a pit stop at airfare deal sites such as Travelzoo, AirfareWatchdog.com and ThePointsGuy.com, to check for mileage bonus offers and promotion codes that can boost the benefits of booking direct. For example, earlier this week, JetBlue released a promo code, redeemable only on its site, for 20 percent off domestic fall fares.
"At least on some of the time, you're going to get a better deal on the airline's site than on any third-party organization," Perkins said.
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It's not all about deals. Even if you don't book there, use the airline's site to check the roster of possible fees on a flight, Young said. The tally tends to be more comprehensive there than on third-party sites, he said. With some airlines, fee waivers and discounts can also vary by where you book. Members of Frontier's free Discount Den program get $5 off fees for each of their first checked and carry-on bags, when they book a fare through the airline's FlyFrontier.com.
—By CNBC's Kelli B. Grant