“Our approach has always been to be extremely cross-platform,” Ilya Fushman, head of product, business and mobile at Dropbox, said in an interview shortly after Apple’s Worldwide Developer Conference, which took place yesterday in San Francisco. “It will be hard for any one ecosystem player. Even Apple.”

The iPhone maker has dabbled in file storage capabilities for several years, but its updated offering will now let users store any type of document in the cloud and then access or collaborate on it from any iOS device and Mac or Windows computers. “iCloud Drive brings a whole new level of collaboration between apps, providing seamless access and the ability to work on the same file across multiple apps,” the company said in a press release issued Monday morning. Files will be available inside Finder, not to mention auto-synced across multiple devices—unless, of course, you use a phone that runs on Google’s (GOOG) Android mobile operating system.

That’s where Dropbox and a growing number of competitors have the upper hand. Apple didn’t say whether it would make iCloud Drive available to users of Android-powered phones, like those made by device makers Samsung and HTC, at some point in the future. Dropbox, meanwhile, lets users of any device and any operating system share documents—even with friends who don’t use Dropbox. That’s at least partly why the growing startup’s simple and easy-to-use file storage and sharing service has amassed a whopping 300 million customers. Dropbox won’t say what percentage of its customers are also iPhone users. But the company’s head of product, Fushman, did say business customers tend to use iPhones more than devices that run on Google’s Android mobile operating system. “I just want to get to my stuff,” says Fushman. “I don’t want to think about the operating system it’s on.”

Of course, Dropbox has its challenges. In recent months the company has worked to make its namesake product more compelling and useful by launching new tools like Carousel, a photo-sharing app, and bringing its Mailbox mobile mail application to Android phones and desktops. Its biggest recent push is Dropbox for Business, a slightly more feature-rich flavor of the company’s bread-and-butter file storage offering that is intended for corporate users, adding IT-friendly features like remote wipe and additional ways for large teams to collaborate on shared documents.”We’re not just thinking about files; we’re thinking about conversations,” Fushman says.

But while Dropbox—not Apple—reigns supreme in the consumer market for file storing and sharing, as it veers into the enterprise storage and collaboration territory, it faces a market full of already entrenched competitors such as Box and Microsoft (MSFT). According to Fushman, Dropbox users already represent over 4 million businesses, though it’s not clear how many of those are actually paying corporate customers vs. rogue employees.

Initially, Apple’s new iCloud Drive is likely to appeal to consumers, not IT departments. And getting everyday users to switch to Apple’s service, even if they already own an iPhone, won’t necessarily be easy. (To wit: Despite the launch of Google’s Drive, Dropbox user numbers have continued to skyrocket.) But it’s clear that Dropbox is working in a market that is becoming commoditized, and it’s more important to find more lucrative customers than worry about Apple’s foray into a service it has mastered for years.