You cannot really swap it out because iCloud is much more deeply integrated into iOS.

That said, you can recreate certain use cases. For example, I have the NextCloud app on my iPhone and it automatically uploads all my photos. It cannot do it in the background like Apple, so I need to explicitly open the app once in a while. The good part is that sharing sets of photos with people outside the Apple ecosystem is easier because NextCloud allows me to send them a link.

You cannot backup your application config with NextCloud though.