I have no idea what you mean. iCloud is permanent storage. Your files and photos are in the cloud and on any synced devices until you delete them from any device, at which point they are removed from all devices. Dropbox works the same way. If I open the Dropbox photo folder and delete a photo, it's removed everywhere.
The only thing I can think of that you could be talking about is that Dropbox is not integrated as tightly with your phone's camera roll. Removing a photo from the camera roll won't remove it from Dropbox. This is more due to API limitations than anything, and Dropbox offers a feature that will automatically remove photos from your phone's camera roll when space gets low.
So yeah, I'm thoroughly confused what you're thinking. All these cloud services have the same approach: your data is in the cloud and can be accessed from any device. What data is local vs remote is largely irrelevant. Apple's solution integrates very tightly with the built-in photos app, as you would expect, while third-parties don't have the same level of seamless access.