In light of the recent WPA2 KRACK exploit (which many device and operating system vendors have yet to address or patch), consider all Wi-Fi connections to be unencrypted for purposes of the question.
On 1 side of the question: a browser web app using enhanced (owner-identifying) HTTPS (shows up as a green lock icon in Firefox)
On the other side of the question: a designated purpose-built mobile device app for the same service using its own encryption and authentication scheme
Assume the developers and admins for both the browser app and the mobile app are competent and vigilant - flaws and exploits in both are detected and fixed quickly. The browser app developers have no control over the browser being used (except marking specific browsers as unsupported or blocking them completely).
Which one provides better safeguards against unauthorized decryption and eavesdropping? Intuitively the mobile app should have stronger safeguards than a browser app as there have been known attacks against HTTPS where the browser is tricked into using a weak encryption scheme (in the most egregious cases, dropping encryption completely for certain elements on the page). A mobile app shouldn't have this problem considering the developer can specify a strong encryption scheme on both the client and server.