In short, Google is giving itself all the permissions it could possibly need to run all of Google services, with the specific limitations that it doesn’t own anything you upload and it can’t use your data beyond running its services.
Dropbox’s language is definitely friendlier than Google’s, but it’s actually more expansive, since it’s more vague. Where Google specifically lists the rights and permissions it needs to run its services using precise legal terminology like “create derivative works,” Dropbox just says you’re giving it “the permissions we need” to run its services.
Lots of cruft has been circulating, because most people some to neglect/not mention this little part from Google’s policy:
You retain ownership of any intellectual property rights that you hold in that content. In short, what belongs to you stays yours.