I think the thing that Azure (which includes Azure Mobile Services as one of its offerings) does to help you is that it takes care of the busy work. Whether that’s the infrastructure side of things with networking, storage and operating systems, or the app platform side of things with frameworks and so on, I don’t want to have to do the stuff that someone else can do better, cheaper and faster than me. This is generically true for pretty much any cloud service though.
Azure Mobile Services allows you to create back ends that can be surfaces in native mobile front-ends, so from a performance point of view, you’re taking advantage of the mobile OS’s native controls and rendering. Almost always a better end-user experience.