Dropbox is more convenient because in Drive, you have to download the files if you want to use it and send to other email addresses. While in Dropbox all of the files are just synced. Dropbox is really easier
I have both, however I think that dropbox is the winner for me. It syncs magically and has great api access for other apps. It's my cloud platform of choice.
Certainly both services have advantages and disadvantages. What they both lack is local encryption which makes it pretty hard to use for sensitive information. Maybe SpiderOak or Tresorit are worthy alternatives because those in fact do encrypt your files before sending them off. Dropbox generally is more integrated into a world of third party application (for example password managers etc.) That's why you might go for Dropbox instead of Google Drive.
However, considering both have their servers in the US and the NSA scandal still having some woes you might want to avoid them altogether. Here is a feature chart of both services: Google Drive vs Dropbox