Competition in the wild is really stressful and as a result people make hard to believe mistakes, especially when they are #2 not #1, such as claiming that the only real iOS app is theirs but not the one developed by the competitors. This kind of approach is technically wrong and has some ethical problems. Pricing, differentiation, offering more functionality, advertising your product, special offers, sponsorships, using social media and all other regular tools can be used in competition but blaming the competitors with sentences like "Do not get cheated by fake apps!!" (oh no!!! too many exclamations, this must be important) is not ethical.
Sentences like "My app is the only real iOS app" just reflects your technical inability and ignorance. Let me tell you the truth; the end user is not interested in what is real or fake (fake=browser according to you). The end user just wants to get the advertised functionality.
Anyway. Let me explain you,this is really simple, what makes an app a real iOS app
- Being approved by Apple and being available on the Apple AppStore
- Being able to run on iOS (iPhone, iPad and iPod Touch), which means your app executes real iOS machine code
- Following the iOS User Interface Design Guidelines
- Being able to use the official iOS APIs and Frameworks such as DocumentInteractionController found in UIKit Framework
See? This is really simple just 4 rules not much or less. Including irrelevant app specific features and wrong performance indicators in a comparison table can make your conclusion seem convincing. But trust me users do not care much about these tables and conclusions especially if it is very clear that you have benefits from this comparisions.
NOTE-1: Browser apps are also real apps since they meet all the 4 criterias I mentioned
NOTE-2: mTouch and mTouch+ are not browser apps but they do have generic browser views to support displaying of unsupported Moodle content/mod/activity
NOTE-3: I'm aware of that the release of moodlEZ caused some uncontrolled stress on you. Take it easy and keep improving your apps and business