You're comparing apples to oranges. Trusted local software and trusted web software aren't the issue. The issue is untrusted software. If you run untrusted native software on a (either non-mobile or non-updated) system, it can usually read and potentially exfiltrate all your files. On the other hand, an untrusted web pages can only access and exfiltrate the files you choose to let them access.
When I create a document locally, or copy a photo from my camera to my computer, I'm responsible for how far it leaks, and it's fairly easy to manage and understand.
When I create similar data in a web app, I have no control over what happens to it.
How is "privacy worse on native"?