Consider two fintech juggernaut stocks: PayPal (PYPL 1.94%), which pioneered online payment processing, and Square (SQ -0.46%), which enabled sellers to take credit card payments with their mobile devices. With the online processor at a market cap of $300 billion-plus and the in-person payment processor at more than $115 billion, is one a better buy today? Fool contributors Matthew Frankel, Brian Feroldi, and Brian Withers discuss on a Fool Live episode, recorded on Feb. 4, why both of these stocks still have plenty of room to grow. 

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Brian Withers: I like Elizabeth's question, PayPal versus Square.

Matthew Frankel: Both.

Brian Feroldi: Yes.

Withers: I own Square and sold off PayPal. Maybe that was my mistake.

Frankel: I own Square. I do not own PayPal anymore. Like I said, I got some shares in the eBay spinoff a while ago and eventually ended up selling those off. I don't really remember. I think it was to pay for my wedding. [laughs] There was a reason I sold them.

But I still have Square. There's room for both to grow. They both operate in pretty different areas. There's obviously some overlap between the business, like Venmo and Cash App are rivals in a lot of ways. But PayPal is generally like the online payment processor. That's their bread and butter. That's where they make most of their money, not Venmo. Although Venmo's kind of the growth engine with a lot of future potential.

Whereas Square is more of an omnichannel. They're really a brick-and-mortar retailer payment processor. But they are trying to build out their omnichannel capabilities. But most Square merchants have a physical presence, which is not necessarily the case for PayPal. They're not necessarily direct competitors but they do compete in a lot of ways. I think there is room for both of them to grow.

I mentioned that PayPal's payment volume has just reached a little over a trillion dollars annually. The global payments market is $185 trillion in size. So we don't think of it as an either-or necessarily. Both of them have considerable room to grow.

Withers: Well, and certainly there is still a ton of the world that uses cash.

Frankel: Yeah, that's true. The majority of transactions around the world are in cash, and especially a lot of places outside of the U.S. We think of credit cards as being universally accepted. That's not the case everywhere. A lot of key markets, a lot of Asia, a lot of Latin America, where credit cards or not universally accepted. Card payments or cashless payments or mobile payments or any of those. A lot of places you still have to pay with cash, so fintech, in general, is still in the early stages of disruption.

Feroldi: How is this for a stat: Square is officially bigger than Goldman Sachs.

Frankel: I believe it.

Feroldi: And Charles Schwab and American Express.

Frankel: Did you know that one-fourth of U.S. Bitcoin volume is now attributed to the Cash App? One-fourth, and that's a small part of Square's business. So when you say it's bigger than Goldman Sachs and they account for one-fourth of Bitcoin volume, I believe it.

Feroldi: Yeah. I mean, they are a $100 billion company. That is huge, and they're are still growing.

Withers: I think it's my third or fourth biggest position, and I'm not selling at all. That's a long-term hold for me.

Frankel: I told Brian a while ago, Withers, that I bought Square before it was fashionable. I got in just after the IPO. My cost basis is $11.02 per share. Back then they were like the little squared card reader that you saw in people's iPhones at a craft market.

Withers: This is a super example of a company that you never could have seen. People ask us, "What's the next 10-bagger? What's the next 100-bagger?" You never would have predicted that Square gone from a little thing that you plug into your phone to this Cash App, to selling. Their Cash App, I think next quarter is going to surpass their small business stuff, which is what they were founded on.

They not only created a new business model, but that business segment that they have: it's growing faster, it's more lucrative, and it's got a bigger addressable market, so who'd have thunk it? You just don't know.

Feroldi: Optionality.