Web apps will be more restricted into terms of how they can interact with the underlying OS as they first have to go through the browser. Also I wouldn’t say weapp have any influence on independence and privacy, and if anything they are less private since the hosting server will know your IP and often require an account to use them. Native apps are installed on the system and unless they have routines to call back to the developer, it won’t really share any information about your system or usage.