The two products are not same; Google Docs is designed for online collaboration while Dropbox is for file sync. Sometime it is very useful to keep bunch of your files sync on different computers. If you are looking for an online storage solution, Google Docs is enough. And there is a client app for Google Docs
However, for us, it will need lots of extra work if we want to use it locally. And what if we need to use it locally at university or work? As mentioned above, this is more of a backup solution and not as good software for storing confidential or sensitive data. If you are looking for any online backup solution, go to Dropbox first. It has a better client app built-in. Dropbox is not a great client app. Also, Dropbox offers no offline storage option for the users. It also doesn't allow to view any files that are shared. It is worth mentioning that Dropbox is actually closed source and can be easily hacked. So the best course of action will be to use online backup solution. If you are looking for a service for free online backup, check out my post where I give the top 10 free online backup solutions. Free Online Backup Software.