Cathie Wood and Warren Buffett are perhaps the two best-known investors of our time.

Buffett has long been considered the greatest investor of all time, having grown his Berkshire Hathaway (BRK.A -1.29%) (BRK.B -1.41%) holding company to be one of the most valuable companies in the world, making early investors rich along with him.

Wood, on the other hand, has made a name for herself quite recently, as her ARK Invest exchange-traded funds (ETFs), including the flagship ARK Innovation ETF (ARKK -2.53%), crushed the market last year, with ARK Innovation jumping 149%. 

As investors, their styles are almost polar opposites. Wood's ETFs trade dozens of stocks everyday, while Buffett says his favorite holding period is forever. Wood looks for disruptive growth stocks, riding new technologies like electric cars, gene editing, space travel, or fintech, among others.

Buffett, meanwhile, is a classic value investor , aiming to find quality companies that are trading below their intrinsic value, and he favors companies with sustainable competitive advantages. In other words, he looks for companies that can't be disrupted.

Warren Buffett with some people behind him.

Warren Buffett. Image source: The Motley Fool.

Unsurprisingly, there is little overlap in holdings between the two, but there are some Cathie Wood stocks that Warren Buffett would likely be glad to call his own. Let's take a look at a few.

1. PayPal

Buffett's favorite kinds of stocks are insurance companies. Berkshire owns GEICO and is an investor in several other insurance companies. Buffett sees insurance as a timeless industry -- people will always need protection for unfortunate events -- and he also loves that the insurance business model allows him to sit back and collect premiums, which he calls float, and reinvest them, essentially taking advantage of free money.

While PayPal (PYPL 0.13%) is not an insurance company, it captures many of the features Buffett likes about the insurance business model. PayPal is a leader in digital payments, facilitating peer-to-peer transactions through apps like Venmo, and offers payments solutions for businesses so they can easily collect and handle transactions.

The company benefits from several competitive advantages, including its well-known brand name as it had a first-mover advantage, and network effects through 377 million active accounts. Like credit card companies, PayPal earns money charging a fee per transaction, and that has proven to be a highly lucrative business.

In 2020, PayPal generated $4.2 billion in net income on $21.5 billion in revenue, or a 19.5% profit margin, demonstrating the kind of wide margins indicative of a competitive advantage. PayPal is also growing quickly, with revenue up 20.7% last year. 

Wood's ARK Invest owns $335 million worth of PayPal in ARK Next Generation Internet ETF (ARKG -0.08%) and ARK Fintech Innovation (ARKF -3.08%). Buffett, who already owns Mastercard and Visa through Berkshire, would find much to admire in PayPal.

2. The Trade Desk

Advertising has long been one of Buffett's favorite business models. For much of his career, he was a big backer of newspapers, including being a major holder in the Washington Post Company, and has owned dozens of other newspapers as well. He's also called newspapers local monopolies, arguing that newspapers in small cities without competition would "gush profits."

More recently, however, as the industry has come under pressure from digital media, Buffett has acknowledged that most newspapers are "toast." 

But the advertising business still remains a fount of profits -- it's just shifted to digital media. One way to take advantage of the technological shift in advertising is through The Trade Desk (TTD -3.12%), an ad tech firm that is the leading pure-play demand side platform (DSP), meaning it helps ad agencies efficiently allocate their budgets across multiple channels.

The Trade Desk operates a cloud-based, self-serve platform that has delivered both high growth and fat profits. Advertising is a high-margin business model at scale, and The Trade Desk has capitalized on that, with few tech companies growing as fast or as profitably as it is. Last year, revenue jumped 26% to $836 million, and it posted adjusted EBITDA of $283.7 million, or a 34% margin. It's hard not to like numbers like that.

The ARK Next Generation Internet ETF owns $166 million in Trade Desk shares. The stock wouldn't look out of place in Berkshire Hathaway's portfolio, given its growth and profits, as well as Buffett's penchant for advertising businesses.

3. Alibaba

Value stocks aren't easy to come by at ARK, but Alibaba (BABA 7.44%) fits the bill as both a growth stock and a value stock. The Chinese tech giant has abundant competitive advantages. It's the world's biggest e-commerce platform with more than $1 trillion in annual gross merchandise volume, built on giant marketplaces like Tmall and Taobao, and it has other growth businesses in areas like logistics and cloud computing.

Alibaba has faced scrutiny from the Chinese government in recent months, which included a $2.8 billion fine from China's anti-monopoly commission, and it's been ordered to sell off some of its media businesses. However, investors cheered the news of the fine as it meant that a dark cloud had been over the stock, and the fact that it's gotten such regulatory attention is a function of its own competitive strength.

In Alibaba's most recent quarter, revenue jumped 37% to $33.8 billion, and it posted adjusted net income of $9.1 billion, equivalent to a profit margin of 27%. In part because of the regulatory concerns and a threat to be potentially delisted from U.S. exchanges, Alibaba shares trade at a price-to-earnings (P/E) ratio of 24, much less than the S&P 500 at a P/E of 42.

Alibaba stock looks like a perfect example of value investing, trading for less than its intrinsic value, and Buffett has shown that he's not afraid of Chinese stocks as he's a major backer of BYD, a Chinese electric carmaker.

ARK owns $154 million worth of Alibaba across three of its ETFs, showing it sees multiple growth avenues and advantages for the Chinese tech giant. There are a lot of reasons it would appeal to an investor like Buffett.