Do people buy more fast food during a period of slow economic growth? If so, is there an investment opportunity in buying stock in the Quick Service Restaurant (QSR) companies that serve it? A comparison of the earnings of Jack in the Box (NASDAQ:JACK) — which reports its third-quarter results after the bell Monday — and Wendy’s (NYSE:WEN) reveals some answers.

The QSR market totaled $166 billion in 2010 and was expected to barely budge in 2011, at a 1% rate to $167.7 billion, according to a March 2011 report from WorldStreetFundamentals.com. The report noted that thanks to the economic downturn, there was significant pent-up demand — 40% of consumers were “not dining out or using takeout as often as they would like.” And the report speculated that by unleashing that demand, QSR industry revenues would recover rapidly as the economy recovered.

The biggest player in the industry is McDonald’s (NYSE:MCD), according to QSR. In 2010, MCD’s sales totaled $32.4 billion — earning it QSR’s top rank — based in part on the strength of its very high $2.4 million in annual sales per store. At No. 4, Wendy’s 2010 sales of $8.3 billion gave it 24% of McDonald’s revenues, or $1.4 million per store. And at No. 15, Jack in the Box’s 2010 sales of $2.9 billion gave it 9% of McDonald’s revenues, or $1.3 million per store.

In 2010, Wendy’s implemented new menu ideas and cut a lagging brand. Among the new ideas were “adding Garden Sensations Salads to the menu and offering a Pair 2 Menu that gave customers a chance to choose among 35 salad combinations for $5,” according to QSR. Wendy’s also added Natural Cut Fries with Sea Salt — tossing out its old fries altogether — and it dumped its Arby’s unit in the first half of 2011.

These changes have contributed to good results. In the third quarter of 2011, Wendy’s adjusted EPS of five cents per share were a penny ahead of the Zacks Consensus Estimate. Wendy’s total revenue grew 1.8% to $611.4 million in the quarter. This was thanks to 3% growth in company-owned restaurants and 1.7% more franchise revenues. Its average transaction was up because of “menu improvements (and) brand repositioning,” according to Zacks.

Meanwhile, Jack in the Box is good at advertising, it added new items to its menu in 2010, and it added low-priced items. According to QSR, Jack in the Box won “another gold Effie Award for its Jack campaign.” Its new menu items included “Breakfast Pita, Pastrami Grilled Sandwich, Really Big Chicken Sandwich, and a Grilled Chicken Sandwich,” wrote QSR. And it added low-priced options such as a $3 Hamburger Deluxe meal.

However, this approach has not been enough to boost JACK’s results. On Monday, before its report, the average analyst estimate was 41 cents per share, up 2.5% from the year before. But this positive expectation follows two consecutive quarters of disappointing results — Jack missed EPS estimates by two cents in its fiscal Q3 and nine cents in its fiscal Q2.

Here’s what the investment choice between Wendy’s and Jack in the Box boils down to:

• Wendy’s: Shrinking, narrow margins; cheap stock. Wendy’s sales have fallen 4.6% in the past 12 months to $2.66 billion, while net income has plunged 223% to $2.9 million — yielding a miniscule 0.1% net profit margin. Its PEG of 0.44 (where a PEG of 1.0 is considered fairly priced) is inexpensive on a forward P/E of 22.7 and expected earnings growth of 52% to 23 cents in 2012.
• Jack in the Box: shrinking, narrow margins; expensive stock. Jack in the Box’s sales have dropped 7% in the past 12 months to $2.3 billion, while its net income declined 46.4% to $62 million — yielding a narrow net margin of 2.75%. Its PEG of 1.43 is expensive on a P/E of 17.1 and expected earnings growth of 12% to $1.73 in fiscal year 2012.

Wendy’s looks like the winner in this fast-food value faceoff. But that success depends heavily on a big turnaround in 2012. Jack in the Box looks like it’s in pretty rough shape, but a better-than-expected third-quarter report could change that.

As of this writing, Peter Cohan did not hold a position in any of the aforementioned stocks.