Dropbox is not an editing app. However, it provides an api that allows other apps to edit files and manage updates to Dropbox files. From within the Dropbox app on iOS you can open files in other apps, just as you can in the Dropbox app on Android.
In fact, you cannot edit many files in the Dropbox app on Android, either. Tap to open an excel spreadsheet and it will ask you which app you want to use to open it (and the same goes for almost every other popular format, including pdf.) Android's sharing of files between apps is much richer than iOS, but iOS has much better apps that interface with Dropbox; you can manage pretty well with either.
(Actually, iOS is better, as you can at least see a read-only view of most files in the Dropbox app. Tap the "open in" control at the top and you can then open the file for editing in another app.)