I also tried using the Dropbox backup approach but it's a massive waste of time syncing endless photos to multiple devices. I don't actually want the files on all my devices, I just want them stored somewhere I can access them later.
So I've started using https://www.everpix.com/ backup from multiple sources Facebook, Flickr, iPhoto, Insagram etc, finds de-duplicates and I don't have to ever worry about running out of storage.
It's a bit annoying since you have to opt each device out, but you can use the Selective Sync feature in Dropbox to not sync your photos folder to each device that you have Dropbox installed on.
So I've started using https://www.everpix.com/ backup from multiple sources Facebook, Flickr, iPhoto, Insagram etc, finds de-duplicates and I don't have to ever worry about running out of storage.