In romance, opposites attract. in business, opposites succeed.

Case in point: American Airlines and Southwest Airlines, two local juggernauts that happen to be the best carriers in the country. (Delta may be larger, after buying Northwest, but both devalued their reputations with bankruptcy.)

For four decades, American and Southwest have been a study in contrasts, clashing over business models and corporate cultures, executive pay, and the bottom line. They’re in the same business, but their propositions couldn’t be more different: Hub-and-spoke vs. point-to-point. First class vs. open seating. Complexity (yield management) vs. simplicity (low fares). Pensions vs. profit-sharing. Chicken cordon bleu vs. peanuts. DFW vs. Dallas Love Field.

You get the idea. In spite of such differences, or maybe because of them, each has won critical acclaim. That makes the conflict of the moment—over airline fees—all the more interesting. American and Southwest have opposing sides on this strategy, yet both are claiming victory.

American brings in almost $1 billion a year in service fees to check bags and change or cancel tickets, according to the Transportation Department. Bag fees increased nearly four-fold from 2007 to 2009, as the airline steadily raised prices. Two years ago, $15 covered the first checked bag; it costs $25 now.

Southwest has not only passed on most fees; they’re at the heart of its value strategy. Southwest mocks fees in TV ads, in the belief that counter-programming will win passengers.

“I hope they charge $100 per bag,” Southwest CEO Gary Kelly said earlier this year. “We will have 100 percent load factors.”

He says the airline picked up 1 point of market share in 2009, a striking achievement while the industry was slashing flights. In the fourth quarter, Southwest cut capacity 8 percent but increased traffic 5 percent, resulting in its 37th straight year of profits. Southwest estimates that the market share gains are worth $500 million to $1 billion in annual revenue.

Kelly says nearly every customer knows “Bags Fly Free.” Just in case, pop-ups on Southwest’s website illustrate the savings on luggage and ticket changes. A research report by Gimme Credit concludes, “Southwest is unique among its peers.” The report’s title: Free is good.

American is just as pleased with its approach, comparing the “unbundling” of products and services to trends in banking, hotels, and other industries. “It has generated a lot of important revenue for us,” American CEO Gerard Arpey said early this year.

So the strategy that gen–erates almost $1 billion in extra revenue for American has been turned 180 degrees by Southwest—and it’s worth a similar amount.
How can that be? In short, they’re catering to different customers.

American (along with Delta, Continental, and other legacy carriers) doesn’t care much about the business Southwest is adding. American says 78 percent of its customers fly just once a year. Most of these leisure travelers are bargain-hunters, buying tickets well in advance and paying a price so low that American often loses money on the deal.

It’s better to have a low-paying customer than none at all. But American can impose fees, and raise them, and risk a little pushback—even defections to Southwest.

It’s business travelers that American cannot alienate, and it takes no chances there. Many fees simply don’t apply to them, not if they’re members of the elite AAdvantage program or buyers of premium tickets. This group travels often, pays higher fares, and rewards American for its global network.

Business customers account for roughly 20 percent of American’s passengers, but their spending makes the traveler’s great life possible—the Admirals Clubs, first-class seats, concierge service, and scores of destinations.

You might think a dual-class system would provoke a backlash. But it’s so well-established in air travel that we even accept certain customers getting whisked through the security line.

Fair or not, it’s business. American started down this road in 2003, after restructuring staved off bankruptcy. A takeaway from that experience was that American had to give customers only what they’d pay for.

American once invested in offering more legroom in coach. Travelers liked the idea but not enough to pay extra, so American had to retrofit planes to squeeze in more customers.

That ended freebies and began an onboard retailing operation. American’s flight attendants now sell sandwiches and drinks, pillows and blankets.

In 2008, American introduced the bag fee and increased most charges. Passengers accepted it, and other airlines followed. Today, most carriers earn hundreds of millions in this high-margin revenue. US Airways charges extra for aisle and window seats, an indication of where fees are headed.

Southwest is edging in. It added a pet fee, and a $10 option to board planes first. Southwest says they’re new services, not dings for typical benefits. How long can it hold out and leave mega-bucks on the table? It depends on how many customers notice.

I usually fly American, but recently chose Southwest for a trip to St. Louis. A relative was facing surgery, but the schedule changed and the ticket had to be re-booked. With Southwest, there was no $150 fee and no charge to talk with an agent. The new ticket was even $9 less.

Vive la difference—for as long as it lasts.

Mitchell Schnurman is the business columnist for the Fort Worth Star-Telegram. For the past five years, his column has been named the “Best in Business” by the Society of American Business Editors and Writers.