PayPal Holdings (NASDAQ:PYPL) and American Express (NYSE:AXP) have both done very well in 2019, but trouble may be on the horizon if the economy starts to slow. Once consumer spending starts to stumble, it could lead to a big correction for these two stocks. Let's take a closer look at these companies to see which one is in better shape to weather a possible recession.

Aggressive growth has helped make PayPal a top performer

PayPal Holdings has evolved over the years from the preferred payment source in the eBay marketplace to a much more widely used platform. Today, PayPal is employed regularly by users of apps like Uber and Spotify, in addition to many other businesses. The payment processor has become a go-to option for many when it comes to digital payments.

With names like Venmo, Bill Me Later, and Hyperwallet, PayPal has been busy with acquisitions over the years that have helped its revenues soar from $9.2 billion in 2015 to $15.5 billion in 2018, an increase of more than 67%. That's been good enough to put PayPal solidly on the Fortune 500 list, almost within the top 200.

Multiple credit cards laid out on a desk.

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PayPal has just come off another strong quarter in which its profits beat expectations and sales were up 19% year over year, to $4.38 billion for the period. The total dollar amount that was processed on its platform reached $178.67 billion, good enough to come in above expectations and arrive at a 25% increase from the prior year. And PayPal has recently secured a license to provide online payment services in China, which could unlock another great growth opportunity.

Over the trailing 12 months, PayPal has accumulated $3.7 billion in free cash flow, which will give it plenty of options should it continue to look for new acquisitions and ways to grow its business. Year-to-date, the stock has risen about 20%, but at a price-to-earnings ratio of nearly 50, investors are paying a big premium to purchase the stock today.

Questions about Amex's growth could make the stock riskier

American Express has benefited from strong consumer buying habits, and it is coming off a strong quarter of its own. But some headwinds have dampened investors' outlook for the payment processor. Not only is there a danger that consumer spending -- which was pivotal in the company's most recent earnings -- could be on the way down, but corporations are looking to trim their budgets too.

Amex's growth has been much more modest than PayPal's over the years; its top line in 2015 was $24.8 billion and in 2018 reached $28.9 billion, an increase of just 16% over the course of three years. And with potentially tougher economic times ahead, growing revenue might not come any easier. For now, though, the company remains optimistic and is still projecting fourth-quarter revenue growth of between 8% and 10%.

Without the same excitement surrounding Amex's growth, investors have been paying more modest multiples for the company, and the stock is currently valued at a price-to-earnings ratio of around 15. Financially, Amex is still in terrific shape, as its free cash flow over the past 12 months has reached more than $7.5 billion.

Why the edge goes to PayPal

PayPal might be the more expensive stock of the two to own today, but for good reason. With a variety of different apps and businesses using its service, the company offers a lot of diversification, so it isn't overly exposed to one segment of the market. And with its healthy free cash flow, investors won't have to worry that the company is going to run into trouble if the economy tightens up.

Both stocks are good investments today, and both have very strong financials. However, the difference comes down to growth, where there's no denying that PayPal has much more potential.