Mobile Web sites should be tested in the similar way as regular sites for HTML, CSS, JavaScript and graphical assets in addition to how much load they have on the database, or content management system (CMS).
Mobile applications may have minimal footprint on the server if most of the user interaction and processing happens in the app, or might have footprint comparable to the mobile Websites. The advantage of course is that no user interface elements are being send from the server, unless the HTML is being generated and "plugged in" as it was in the early versions of GMail which had vertical list of web browser elements.
