HTML5 vs Native Apps
Native to the browser - Apps can be displayed in the browser which makes it available on all devices and systems including desktops
Can be written once and used on any device and OS - Only one version of the app needs to be created and can run anywhere. Native apps need an iPhone version, an Android version, etc
Much Lower Costs - HTML5 apps are MUCH cheaper as they are easier to develop and you only need one version of the app
In my own opinion, I think there is a place for both types of web apps. If you
No Approval - HTML5 apps do not need to get "approved" by the app store
No Downloads - Most HTML5 apps do not need you to download anything unlike native apps
Native App Advantages
More Professional - Having an app publiched in the App Store looks more professional and commercial
More Reliable - Native app development is more complicated in terms of programming BUT that usually means the programmers know what they're doing. It most likley is not a high school kid building his first Hello World application like it could be with HTML.
No Need For an Internet Connection - Many native apps can be used without an Internet connection. HTML5 apps will because they run in a browser
Faster - Native apps are generally faster than HTML5, usually by around 15%-20%.
Better Device Integration - Native apps are usually more effective at integrating the capabilities of the device into the app itself, such as GPS, Camera and Voice Recorders. In native apps, images, GPS coordinates, voice memos, etc can be piped directly into the database without users needing to search and attach them.