One thing that I dislike about native apps over web apps is there is no way to tell how securely credentials are being passed over wifi or a mobile network. With websites you can make sure the connection is HTTPS from the browser and be pretty sure no one who can sniff your network traffic can see what you're doing.

I'd hope that in this day and age every native app, especially those of a banking nature, is using HTTPS where appropriate but (without sniffing your own network) there is no way to tell.