PayPal Holdings (NASDAQ:PYPL) and American Express (NYSE:AXP) are two intriguing investments to consider in the payments industry. Both companies are well positioned to deliver attractive returns, but they're also quite different in areas such as growth potential, valuation, and capital distributions.

Which one is a better purchase for investors right now: PayPal or American Express? 

PayPal is booming
PayPal is a market leader in digital payments, a remarkably compelling industry offering enormous potential for growth over the years ahead. Management is doing a sound job at capitalizing on its opportunities, and the business is clearly firing on all cylinders, both from an operational and financial point of view. 

The company ended the fourth quarter of 2015 with 179 million active customer accounts, an increase of 11% versus the same quarter in 2014. PayPal processed $1.4 billion payment transactions during the quarter, an increase of 25% versus the same quarter in the prior year.  Since the amount of transactions is growing at a faster rate than the user count, this signals that engagement per user is on the rise, a healthy sign in terms of measuring PayPal's ability to sustain growth. Payment transactions per active account grew 25% year over year in the last quarter of 2015.

Total payment volume was a staggering $81.5 billion during the quarter, an increase of 23% in U.S. dollars and an even stronger jump of 29% versus the same quarter last year. Net revenue during the quarter was $2.56 billion, an increase of 17% in U.S. dollars and a 21% growth rate when leaving currency fluctuations aside. The business model is remarkably profitable, PayPal delivered an operating margin around 16% of revenue, and adjusted operating margin was a staggering 21% of sales last quarter.

Financial performance doesn't leave much to be desired, but it's important to keep in mind that PayPal stock is priced at a premium versus the overall market. The company carries a forward price-to-earnings ratio of 23 times earnings forecasts for the coming year. As a reference, the average company in the S&P 500 index trades at a forward price-to-earnings ratio in the area of 17. PayPal clearly deserves an above-average valuation due to its superior growth prospects, but investors looking for bargains in the stock market may be more inclined toward other alternatives. 

American Express looks undervalued
American Express is one of the most traditional players in the credit cards business. The company owns one of the most valuable brands in the industry, and it has a particularly affluent customer base, this means lower credit risk and more negotiating power with merchants. 

However, while the business is fundamentally solid, the company is not doing very well lately. American Express lost its position as the exclusive credit card accepted at Costco Wholesale last year, and the two companies also ended their agreement to co-brand the TrueEarnings card. In addition, airline operator JetBlue dropped American Express as its co-branded card partner in February of 2015.

Being a big market player in a mature industry, it's not easy for American Express to compensate for this lost businesses via new growth ventures, and the company's financial performance has been disappointing lately. Total revenue during the fourth quarter of 2015 declined by 9% to $8.4 billion, while net income fell 12% year over year. Management is also expecting modest earnings growth in 2016 and 2017, so investors don't have many reasons to expect accelerating performance from American Express anytime soon.

The good news is, these difficulties are already incorporated into valuation to a good degree, and American Express is priced at conveniently low levels. The stock trades at a forward price-to-earnings ratio around 11 times forecasted earnings, which is nearly half the valuation currently being assigned to PayPal. Besides, American Express pays a dividend yield of 2% at current prices, while PayPal distributes no dividends at all. 

PayPal or American Express?
Investment decisions cannot be analyzed in a vacuum, since the right stock to buy would depend on factors such as an investor's risk tolerance, investment strategy, and overall vision for the two companies. If you're looking for a solid financial powerhouse with a sustainable dividend that's trading at attractive valuation levels, American Express is the way to go.

On the other hand, PayPal offers far superior growth prospects, and management is doing a rock-solid job at translating the company's opportunities into amazing financial performance for investors. Even if the stock is more expensive, chances are, PayPal will deliver higher returns than American Express over the years ahead. 

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.