Not to defend Snapchat's reputation or anything...but all Dropbox does is 'store files'. Saying snapchat just 'moves pictures' around and therefore shouldn't be valued so highly kind of misses the point. That being said, there are other reasons Snapchat probably shouldn't be valued so highly.
That's a very short-sighted value. Even if you don't believe that there is no value in providing a very convenient and easy-to-use file hosting and file-sharing service that even supports collaboration, just having access to so much personal information is already quite valuable.
And people actually pay for this, to the point that Dropbox is profitable as it is.
Dropbox does a lot more than just store files. It provides a valuable abstraction over universal storage, through its integration with various services. For example, integration with MS Office to provide a single virtual drive to save my work to a single location from any PC i use.
And snapchat provides a valuable abstraction over picture moving that many people use. Does something need to integrate with MS office in order to be useful?
No but integrating with MS Office increases the likelihood that it’s valuable. Utility != value. Always ask yourself: who is my user? Am I providing them with a painkiller or a vitamin?