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The credit card industry has evolved over the decades. American Express (AXP -0.08%) has established a reputation for serving high-end consumers with no-limit charge cards that in some cases require expensive membership fees. Discover Financial (DFS 3.65%) aimed at a different target audience, pioneering the idea of the cash-back card that has become an industrywide staple. As new competitive threats have emerged, both Discover and AmEx have had to respond in ways that would protect their respective franchises. Let's look more closely at American Express and Discover Financial, using a range of common metrics to evaluate their merits.

Stock performance and valuation

Looking at their recent stock returns, neither American Express nor Discover has delivered the performance that investors would have wanted to see. Discover Financial shares are down 6% over the past year, and American Express has suffered an even larger 20% loss over the same time period.

Even though Discover's stock has held better than American Express, investors still don't value the cashback card specialist's shares as highly using simple valuation metrics. On the basis of trailing earnings, Discover has an earnings multiple of just 11. That's not too much less than the trailing P/E ratio of 13 that American Express carries, but it nevertheless shows just how out of favor both companies are compared to the much higher earnings multiple that their peers in the credit card industry currently carry.

The situation doesn't change much when you look at forward earnings projections. Discover has a forward earnings multiple of just over 9, compared to around 11.5 for AmEx. The disparity isn't huge, but Discover ekes out a win on valuation and stock performance over American Express.

Dividends

Many investors like to evaluate stocks based on dividends, and American Express and Discover Financial compare fairly closely on the dividend front. Discover has a slightly higher yield of about 2%, but the 1.8% dividend yield that American Express stock currently pays isn't too far behind.

Neither company is terribly generous in making dividend payments. Both Discover and AmEx pay out between 20% and 25% of their earnings in dividends. That leaves both companies with plenty of room to consider future increases, but neither has shown much inclination to make major changes to their respective dividend policies in terms of dramatically boosting the percentage of earnings that they pay out.

However, one area in which Discover shines is in its commitment to boost its dividend considerably in recent years. After cutting its dividend during the financial crisis, Discover has made six dividend increases that have taken its quarterly payout from $0.02 per share to $0.28. AmEx has also made sizable increases, but its current $0.29 per share payout is only about 60% higher than it was in 2008. The edge is slight, but Discover arguably takes the dividend category as well.

Growth

Both American Express and Discover have some challenges that they'll need to address in their quests for future growth. For American Express, the loss of its relationship with Costco Wholesale will have a disruptive impact on earnings for the near future. The company has also cited lower gasoline prices and airline ticket fares as eating into its revenue, and the need to spend more on marketing in order to attract new customers could put pressure on American Express' bottom line at least for the remainder of 2016 if not longer. Still, American Express has entered into partnerships with companies that have close ties to millennials, and the card giant hopes that its efforts will produce new cardmembers that in turn will become longtime customers to drive American Express' future growth.

Discover has also had to work hard to come out of the shadows of larger card networks. The company still struggles from a lack of universal acceptance, with many merchants who take American Express and other major cards choosing not to take Discover's cards. Yet from a consumer standpoint, Discover's commitment to cashback rewards has given it a sterling reputation, and those who follow the stock believe that the card company should be able to cash in on that reputation by finding new ways to attract both merchants and cardholders.

Both American Express and Discover Financial have encountered obstacles to their growth, but they've also plotted plans to emerge stronger from their struggles. Currently, Discover Financial looks like the better buy based on these metrics, but in the rapidly growing payment services business, there's ample opportunity for more than one player in the space to bounce back and produce strong returns for shareholders.