Dropbox has a library called Chooser, which makes it easy to select files in Dropbox from custom Mobile apps. ( https://www.dropbox.com/developers/chooser#ios )

Dropbox Chooser uses mobile deep link bidirectionally to move between a custom app and the Dropbox app. As for Box app, mobile deep link is one-way; the Box app can be opened but it is not possible to select files and go back to the custom app.

The major advantages of using Dropbox Chooser for service providers are as follows.
- No need to make additional UI for the file chooser
- No need to authenticate or handle tokens

With these advantages, the effort for development can be greatly reduced, and it becomes easy to integrate Dropbox with the service providers custom apps.

Although Box has UI SDKs for mobile, Share SDK and Browse SDK for iOS are in maintenance mode and cannot be actually used. (I wasn’t able to build and run the examples included in those UI SDKs with the latest xcode in my mac)
Even if those UI SDKs can be used, it won’t be possible to drastically reduce the effort for development, because it is necessary to provide certain amount of code for authentication.

From the perspective of eco-solutions, this has been a box's disadvantage against Dropbox.
Please develop easy file share feature like Dropbox Chooser.