That topic of native vs html5 can be seen
here..
My reason is kinda one sided...but native provides unlimited possibilities in your apps... never really tried html5 that much but native code executes faster... there are a bounty of libraries one can use and some more are said in the post i pasted..
Azure, kinvey, Amazon Web Services and so on can be used to supplement back-end code... meaning if you are to build out a app that is heavily dependent on an database and other sever dependent task.. you don't need to code it from scratch you can access those services via an sdk.
Example in Azure, if you were to build an app that needs user reg...login...data storage...push notifications...location services.. media storage.. you can access these features fast without building out a web app that will carry out these tasks. Cut developer time in half.
Sample apps i don't have any sample code that is great but i have a app on windows phone store and working on android apps for myself...other apps i made is for clients.
My advice: Join Android, Windows Phone and Iphone dev forums, blogs and other sites...
See windows phone example code..
here