High trust provider hosted app vs SharePoint hosted app

Go for PHS if you want to write back end code. e.g using CSOM. Here you can use permission elevation or impersonation.

If you don't want to write back end code, only jsom or rest is suitable, also no permission elevation is required go for SHA

The main difference between different types of apps lies in their hosting pattern. If you wanna have your hosting and app deployment in on-premise SharePoint 2013 server only, then you can go with SharePoint-Hosted Apps.

For your custom web parts , you can go with SharePoint hosted app in which case you have to create app-domain(using Power-shell) and add a app prefix in central admin & then register your app in app-domain.

Provider-hosted comes in two flavors viz a) High trust Provider-hosted app where you need to create a certificate for creating the trust between your remote web application and SharePoint server and then you can register and publish your app in SharePoint by creating Client ID & Client Secret b) Azure based Provider-hosted app where you will need a tenant account on windows azure portal (www.windowsazure.com) & SharePoint online account (you can have free account also for 30 days). Here , you can download the publish profile of azure website and import that while publishing your application. Just validate the connection with proper settings (Service URL , Destination URL etc) and your app will be hosted in Azure website.https://social.msdn.microsoft.com/Forums/officeapps/en-US/06c183eb-68bd-4f26-8696-bf3434105478/provider-hosted-apps-vs-sharepoint-hosted-apps?forum=appsforsharepoint

Also check this one Is there a difference between a Sharepoint Hosted App and a Cloud Hosted App?