I think the biggest difference here is that the iCloud Photo Library functionality will back up/sync new photos but won't delete existing photos unless you explicitly tell it to do so, which prevents data loss from corrupted or accidentally deleted local files (which Dropbox will cheerfully sync along to each other machine you have).
Dropbox isn't even close to this experience. Yes the files themselves would be everywhere, but I don't want to have to go into the Dropbox app to view my photos (not to mention the Dropbox app being extremely slow in my experience). With iCloud they're all in your regular Photos app ready to be shared or used in other apps just like the photos you shot with your phone.
Not being able to have another app fix issues in the stock app is a problem.
If dropbox were able to express an intent to be notified of all photos taken, they could have solved this problem long ago and roughly as well, but they couldn't and so didn't. The problem is not that Apple solved this problem, but that no one else could have due to how apple treats all non-apple apps as second class citizens.
That's a probably a limitation of iOS. E.g. on my Android phone, I sync photos with Bittorrent sync. I can view them using the gallery app, like any other photo.
Sure, Dropbox will allow access to the files across all your devices. But it doesn't expose the photo metadata -- things like location, date/time, face recognition -- in a way that lets you filter meaningfully.
