On Thursday morning, two of the top four U.S. airlines -- United Continental (NYSE:UAL) and Southwest Airlines (NYSE:LUV) -- will release their third-quarter earnings reports. Both companies are expected to post record profits for the third quarter and for 2015 as a whole.

However, the two rivals are facing different opportunities and challenges right now. Let's review what investors should be looking for in these earnings reports and the companies' conference calls.

United faces another crisis
United Continental is in the midst of a leadership crisis. Former CEO Jeff Smisek resigned last month amid a scandal. His replacement, Oscar Munoz, suffered a heart attack last week that has put him on the sidelines indefinitely.

Airline United Continental Ual Airbus A

United Airlines is facing a leadership void. Photo: The Motley Fool.

This turmoil would not be good for any company, but it's particularly problematic for United, which is still in the middle of a multi-year turnaround effort. A key question for the management team will concern Munoz's prognosis and the company's contingency plans in the event that Munoz can't return for many months -- or at all.

Aside from the uncertain CEO situation, another key question will be the pace of improvement in United's unit revenue trajectory. Passenger revenue per available seat mile (PRASM) fell 5.6% year over year in Q2, hurt by the strong dollar, falling international fuel surcharges, and plummeting energy sector demand. United has estimated that PRASM declined by 5.5%-6% in Q3.

Many of the headwinds that have hurt United's PRASM in the past few quarters will continue in the fourth quarter before starting to level out in 2016. However, United announced in July that it had started making significant schedule cuts in its weaker markets. The key question is whether those were enough to slow the pace of its unit revenue declines. If not, investors should look for United to cut capacity again for Q1.

Despite all of these issues, analysts currently expect United to post earnings per share of $4.55, up 65% year over year. The stock trades for less than five times United's projected 2015 pre-tax earnings, which means the bar is set very low.

Southwest Airlines continues its growth
While United's leadership crisis threatens to overshadow its record earnings, there is little to complain about at Southwest Airlines. The company's profit margin is soaring as fuel prices continue to fall, while unit revenue has started stabilizing.

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Southwest Airlines has been firing on all cylinders lately. Photo: The Motley Fool.

For Q3, Southwest increased its capacity 7.6% year over year. Since revenue per available seat mile declined by roughly only 1%, Southwest should post robust mid- to high-single-digit revenue growth for the quarter. Analysts expect EPS to jump 67% to $0.92.

The low-fare leader will continue its growth in Q4, with an increasing focus on international markets. Last week, Southwest opened its new five-gate international concourse in Houston and launched six new routes from Houston to Mexico and Central America. Another two routes will start up in early November.

Southwest's management may provide some color about how those new routes are shaping up during the company's quarterly earnings call. Investors should also watch for any details on Southwest's international growth plans for 2016.

Finally, in August, Southwest completed a year-long process of growing its presence in Dallas after its hometown airport, Love Field, opened to long-haul flights. Southwest is lapping the first wave of its growth in Dallas during the fourth quarter. This could set the stage for solid unit revenue growth in Dallas over the next year or two as the new routes mature. Investors should be on the lookout for any management commentary about that process.

In short, United Continental investors should be looking for signs that in CEO Oscar Munoz's absence, the rest of the management team has things under control -- or not. By contrast, there are no major issues threatening Southwest's prospects right now. Southwest Airlines investors should therefore be looking for more information on the company's growth plans.

Adam Levine-Weinberg owns shares of United Continental Holdings, The Motley Fool has no position in any of the stocks mentioned. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.