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 cost, you'd think American airlines would be ultra-profitable, and American Airlines stock cheap from a valuation perspective.

You'd be right.

Delta Air Lines (NYSE:DAL) earned more than $4.5 billion in net profits last year. American Airlines Group (NASDAQ:AAL) did even better, raking in $7.6 billion in profits. Despite rolling in the dough, though, both of these stocks are getting rolled by investors. Delta shares are actually down over the past year, for example. And over the past 52 weeks, American Airlines stock is down, too -- 22%!

Of course, for opportunistic investors, all of this is good news. If you agree that low oil prices are going to hang around for a good long while, allowing airlines to continue earning beaucoup bucks, this all gives us the opportunity to profit handsomely from buying cheap airline stocks. But which one is the better buy? Delta Air Lines or American Airlines?

Let's take a look.

Delta Air Lines
Priced at just 8 times trailing earnings today, and expected to grow profits so fast that its forward P/E will fall to 6.3, Delta Air Lines stock looks undeniably cheap. The stock's growing like a weed, with analysts quoted on S&P Global Market Intelligence predicting long-term earnings growth of 27% annually over the next five years.

Perhaps best of all for investors who like to earn an income from their stocks, Delta Air Lines pays one of the best dividends in the business, a thumping 1.3% annually.

American Airlines
And yet, as good as Delta looks, American Airlines looks even better. American's trailing P/E ratio of 3.3  is less than half what Delta costs. American's dividend yield is 1.1% -- perfectly respectable, and not that far behind Delta.

Growth-wise, you could argue that the 9% rate of earnings growth analysts are looking for from American Airlines is slower than Delta's 27% -- because it is. On the other hand, you could also argue that 9% is a much more realistic rate of growth to expect from a large, mature business like an international airline. And you could argue that with everyone expecting "only" 9% growth out of American, the stock stands a better chance of surprising investors with better-than-expected growth -- because it does!

Deciding factor
When you get right down to it, though, that uncertainty about the future tells me that between these two stocks, Delta is still the better buy. Whether you're talking earnings, growth in earnings, or the future of oil prices in 2016 and beyond, the future's uncertain -- but one thing is clear...

When you're investing in a stock, safer is often better. And to my Foolish eye, it's much safer to invest in a company that carries modest debt than to buy a stock that's deep in hock. Currently, Delta carries a debt load of $8.6 billion, which is a whole lot more than nothing. On the other hand, Delta also has $3.4 billion in cash on the books, and at last report, it was generating nearly $5 billion in new free cash flow annually. Theoretically, at least, Delta has the ability to wipe out nearly all of its debt load in just one year's time, if it were so inclined.

You can't say the same thing about American Airlines. American hasn't yet reported its full-year 2015 free cash flow, but over the three quarters of 2015 it has reported on, FCF totaled just $1.4 billion. That's a nice improvement over the company's more recent record of burning cash in every year for the past five years (according to S&P Global Market Intelligence data). But even so, it's not enough money to make much of a dent in American Airlines' monster $20.6 billion debt load.

Even assuming American maintains its current rate of cash production, and netting out the company's $6.2 billion in cash already accumulated, this airline has so much debt already that it would take the company more than seven years to pay it all back at current rates of cash production. To me, that makes American Airlines a significantly riskier stock to own -- and it makes Delta Air Lines the better buy.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.