Google Drive and Dropbox are both quite safe, and definitely a good back-up option for your book, but they shouldn't be your only option. Always have multiple back-up locations--flash drives (which will fail, yes), external hard-drives (which also fail, but not as frequently if you buy good ones, which aren't actually that expensive), multiple different cloud storages, and hard copies never hurt anyone either.
Google Drive is bigger than Dropbox. It's 15GB to begin with and you can get more periodically even without paying (Google gives out 2GB sometimes for checking your security settings). It also integrates nicely with Gmail if you happen to use that. I use Dropbox as well, but Dropbox's other big drawback is that it's an absolute RAM hog. It likes to run all the time, which doesn't help and getting it off your computer can also be a bit of a trick.