The two companies have been competing for over a decade in the market of cloud file storage, with both benefiting from the rapid move to mobile devices and the need to access data from anywhere at all hours of the day.
Box CEO Aaron Levie has insisted that his company is more focused on working with big businesses than is Dropbox, but investors clearly recognize the threat. Dropbox gained wide adoption in the consumer market with a product that has free and paid tiers and started getting traction in businesses as users brought the app to work.
Box is one of seven competitors that Dropbox lists in its IPO prospectus, along with much bigger companies like Amazon, Google, Apple and Microsoft. Dropbox says it competes with Box "on a more limited basis" for enterprise customers.
Dropbox shares jumped as much as 50 percent from their IPO price of $21 to as high as $31.60, giving the company a stock market value of over $12 billion. At the end of the trading day, Box was valued at $2.8 billion.
Until Friday, Dropbox had faced criticism for not living up to its $10 billion valuation from 2014, and investors had marked down their private Dropbox shares in recent years.
Dropbox said in its prospectus that is has 500 million registered users, but only 11 million paying subscribers. About 30 percent of those are on a business plan.
"That's around kind of $330 million or so in revenue as compared to our $500 million, which is entirely enterprise-driven," Levie said about Dropbox at the Morgan Stanley Technology, Media and Telecom conference in San Francisco earlier this month.
Dropbox CEO Drew Houston has also occasionally spoken about how the company is distinct from Box.
"We've got a competitor out there, they're like, oh, we're Dropbox for the enterprise," he said, referring to Box, at a 2015 company event, as Wired reported. "But the challenge is they don't have that kind of bottom-up adoption."
Box shares fell sharply early this month after the company issued a weaker revenue forecast than analysts expected for its fiscal quarter.