Your files never leave your device
With a server-based converter, your document travels across the internet to someone else's machine, gets processed, and then comes back. During that round trip, the file sits on a server you don't control even if it's deleted after processing, the intermediate state is out of your hands.
Browser-based conversion happens inside your tab. The document stays in your browser's memory for the duration of the operation and is discarded when you close the tab. There is no copy on a remote server, no log of the file, no window where someone else's system has access to it. For confidential documents contracts, NDAs, financial reports, medical records this is not a luxury. It's a requirement.