Typical business case scenarios for SharePoint 2013 Apps

Question

What are the typical real time business case scenario for 1. SharePoint Hosted apps 2. Auto Hosted apps 3. provider hosted Apps? Why people choose any of this model apps model in comparison to typical On-Premise solution? 
Another question comes is when should one go for On-Premise solution rather than Apps? What are real time scenarios?

Answer 1

Let's discuss first whether to develop apps or full trust solution.
Talking about technical aspect, On-Premise solution is popular choice for organizations who have SharePoint hosted on premise (not SharePoint Online). However, if you are using SharePoint Online, there's no choice except Apps (and possibly sandbox but deprecated).
So for SharePoint Online only viable solution is developing apps. However for on-premise you can develop full trust or apps. However since apps requires a bit more configuration and not yet full feature set as you can do with full trust, most people are still
developing full trust solution on premise.
Talking about business requirement at hand, you can develop apps (even in on-premise), if your requirement is really looks like an app. For example, you would like to develop a SharePoint solution, that will show data from SAP inside SharePoint. The solution
mostly nothing to do with SharePoint but calling SAP services to perform stuffs. So you can develop an apps and deploy inside SharePoint. Another example is import CSV files in SharePoint list, you can write an apps. But mostly I think you need to decide whether
to develop apps depends on the Apps API ability. The API is still very limited in features/functionalities. So even if your requirement looks like apps you can't develop apps if the current SharePoint Apps API doesn't support the functionality. 
Now let's talk about which apps model you would like to use SharePoint Hosted apps means everything hosted inside SharePoint and no other external infrastructure is required. One example is the CSV file upload apps. However, with SharePoint hosted apps,
you can't use C# rather you just have javascript to develop the apps. There's rumours that auto hosted apps will be deprecated not sure but there's not more conceptual difference apart from where the apps is hosted (both hosted outside SharePoint). Provider/auto-hosted
apps will be running outside SharePoint (i.e., in IIS web site), and communicate to SharePoint through REST or client object model. One provider hosted apps in the office app market is adlib pdf conversion. The apps allows you to select multiple files and
covert them to pdf file. Basically the conversion site is hosted somewhere outside (in the provider's infrastructure). When you select all the files and click 'convert' from ribbon user is redirected to the provider site (different url) and the files are merged
and converted to pdf. Since it's outside of sharepoint, you can use any development language (C#, java, php etc.). The provider hosted app talks to sharepoint through REST or client object model.
So in summary, sharepoint hosted app has less complexity as it doesn't require another infrastructure and runs inside sharepoint. However you are limited to use only javascript to develop your apps. On the other hand with provider hosted apps, you can use
any development language but you need to consider extra level of security/complexity to integrate the app with sharepoint.
Thanks,
Sohel Rana
http://ranaictiu-technicalblog.blogspot.com
Thanks for this nice reply. Plz clarify if only Auto hosted apps will be deprecated or provider hosted apps also may be deprecated by MS?