There have been several reviews on Dropbox and how folks in the commercial real estate industry can utilize its features most effectively.
Over the last 90 days, I've had the opportunity to use both Dropbox and Box and wanted to give you my thoughts on how the two compare.

The largest difference between Dropbox and Box is Dropbox is more of a personal file backup and sharing application, whereas Box is more of an enterprise electronic document management application.

I am not the first one to make this observation (see this same question on Quora), but let me make it more specific to the commercial real estate industry.

DROPBOX
I use Dropbox to backup files which I can't risk losing if my computer were to bomb, and ones I don't think I'll need for awhile (if ever), but don't want to risk deleting altogether.

Why use Dropbox for these uses? Mostly because, after installing the software, file syncing is drop dead simple.

Dropbox also allows me to more easily share these files with others, by using sharable links. This feature is great when files are too large to email, or you just don't want to waste email storage capacity.

Users can also share entire folders, but this option gives the outside user substantial control and access to the files within this folder. So, while it is good for collaboration, it isn't great for other uses which require more control.

For a more thorough explanation of Dropbox's features, see CREOutsider's "Dropbox in Plain English" post.

BOX
I use Box to deliver monthly reports to various equity partners and lenders. While Box's file syncing isn't as simple to set up as Dropbox (honestly, I haven't set syncing up on Box because the drag and drop functionality works so well) its file renaming, folder set up and sorting are great for organizing content, which is critical for monthly reporting. Box also makes it very easy to share files and folders using links or granting access and sending notifications via email.

Box also allows administrators to add "collaborators". For each collaborator, you can grant granular level access to folders and files (i.e. preview only, download, upload, edit, etc.) as well as track when users view, download or upload files. This is also great for monthly reporting for auditing and/or documentation purposes. (Yes, I uploaded the file on Monday and you viewed it on Tuesday...)

Box also allows users the ability to post comments and create discussion threads on specific documents, as well as assign tasks (i.e. please approve this budget by next Monday).

As far as mobility is concerned, last August, Box rolled out an HTML5 mobile site which works ok. After testing it against Box's iPhone app, the native app outperforms its HTML5 counterpart in my opinion.

When comparing the native iPhone Box app against Dropbox's, I couldn't see much difference. Both are fluid and easy to use. In this instance, ultimately, the functionality comes down to which product offering suits your needs better, rather than which app outperforms the other.

At the end of the day, I think SmallCloudBuilder.com's comparison of the two services sums it up best:

If you’re in need of a solid business based cloud solution with lots of access controls, Box is the obvious program of choice. But if you are looking for a drag and drop [simple] file sharing solution without all of the bells and whistles, Dropbox provides a great solution.