Who's the best buy in airline stocks today? Here's a hint. Image source: Boeing.

With oil prices in the tank, and jet fuel costing just pennies on the dollar compared to what it used to, you'd think that American airlines would be ultra-profitable, and American airline stocks cheap.

You'd be right.

Delta Air Lines, Inc. (NYSE:DAL), for example, earned more than $4.5 billion in net profits last year, and $4.7 billion over the past 12 months. Southwest Airlines Co. (NYSE:LUV) didn't do quite that well, earning "only" $2.2 billion in profits (on about half as much revenue as Delta raked in). Regardless, investors are showing a whole lot more "LUV" for Southwest stock, which is up 15% over the past 52 weeks.

Delta is up just 3%.

If you're an investor, that divergence in fortunes probably sets your mental gears to turning. Does Southwest's outperformance compared to Delta mean that Southwest is the better company, and Southwest the better stock? Or does Delta's lagging stock price mean there's more room to run at the legacy airline? Put simply: Which stock is the better buy: Delta Air Lines or Southwest?

Let's take a look.

Delta Air Lines

Priced at just 7.2 times trailing earnings today, Delta hasn't gained much lift from its solid Q1 earnings. To the contrary, valued on P/E, Delta stock is cheaper today than it was back in March, before earnings came out.

Partly, that's because of the company's prospects dimming. You see, profits may have been up last quarter, but free cash flow was down, and significantly. Whereas three months ago, Delta was churning out cash profits at the rate of $5 billion a year, data from S&P Global Market Intelligence show that, as of Q1, its annualized rate of free cash flow production has dropped to just $4.1 billion. That's just $0.86 in actual cash profit per $1 of GAAP-reported net income.

Moreover, analysts who follow the company, and who were positing a 27% annualized profits growth rate for the company just a few months ago, now believe that growth rate will be closer to 17%. 

Southwest Airlines

The situation at Southwest is a bit different. Analysts on average see Southwest as the slower grower, predicting 13% long-term growth for Southwest, versus 17% for Delta. But like Delta, Southwest is getting more profitable over time, earning $58 million more net income in Q1 2016 than it did in Q1 2015 and pushing its profitability well above $2.2 billion for the past 12 months.

As far as cash profits go, Southwest generated $1.4 billion over the past year. That's only 63% of the company's reported earnings. On the plus side, though, whereas Delta's free cash flow number declined over the past three months, Southwest's FCF is growing.

And the best airline stock is...

Now which of these two airline stocks is the better buy? You may be surprised to hear this, but while Southwest has by far the better reputation among travelers (scoring 781 out of a possible 1,000 points in J.D. Power's latest rankings of customer satisfaction compared to Delta's 709), I actually think Delta stock is the better investment. Here's why:

Southwest has some undeniable advantages over Delta. It carries a lighter debt load, it's growing free cash flow rather than shrinking it, and, of course, it's the fan favorite among customers. All that said, as investors we're more focused on valuation than on popularity, and at 7.2 times earnings versus Southwest's 12.4, Delta is by far the cheaper stock.

Delta's also the faster-growing stock, and the stock that generates the most free cash flow relative to its reported net income -- indicating a better quality of earnings. Perhaps best of all, Delta boasts one of the best dividends to be found anywhere in the airline industry, paying out more than 1.2% of its profits to shareholders every year. Southwest pays only 0.7%.

On balance, and being guided solely by the numbers, I'm declaring Delta stock the winner in this contest. It's clearly a better buy than Southwest stock.