I remember that in Visual Studio 2010 there was "Replace matching files with local copies" checkbox
Where this checkbox/radiobutton in Visual Studio 2015 ?
In VS2015 it's not possible to set this option in the Publish Window.
But we can do it in another way. Right Click on Project->Properties->Package/Publish Web->Items to deploy
According to MSDN you we have these options
Only files needed to run this application. This is the default value. Visual Studio tries to determine which files are required for the application to run successfully. For example, this includes assemblies in the bin folder, files generated during the build, and files marked as Content. To see if a file is marked as Content, select the file in Solution Explorer, and check the file's Build Action property in the Properties window. You can change the Build Action value to Content to cause the file to be deployed, or change it to something else, such as None, to prevent the file from being deployed. Some file types that are automatically set to Content include .master, .svc, .ashx, .asax, .skin, .browser, .config, .and sitemap. A file must be included in the project in order to have a Build Action property.
All files in this project. Visual Studio deploys all files that are included in the project, regardless of their Build Action property values.
All files in the project folder. Visual Studio deploys all files that are in the project folder and subfolders, regardless of whether they are included in the project or their Build Action property values.
UPDATE
I figured out another method how to update all files during publishing. I faced issue when some of my files were not updated properly (config,ascx and etc.), in my inetpub folder I had old version of files. So first I published site in another new folder and then replace files in inetpub folder with files from new folder.