While these two languages are sometimes compared and even thought of as competitors, they're actually complimentary languages and are typically used in conjunction to build fast and interactive web applications. In more precise terms, PHP typically handles the back-end while JavaScript handles the front-end
Rhetoric of course. 😉 Any coding language (either directed or bent over as frontend or backend) that is able to perform network connection is suitable for such use (i.e. all languages in fact).
As Здравко said, you can use any language to access the Dropbox API as long as it can make network requests.
For reference, Dropbox offers an official SDK for JavaScript, but not PHP. Using an SDK can make integrating with the Dropbox API easier. Use of an SDK for accessing the Dropbox API is optional though.
