Background first: I have a database-first EF6 model in Visual Studio 2015 (latest nuget 6.1.3 pointing to a local SQL Server 2014 SP1 Express database) on a Windows 10 Pro lapto
I can't comment as I'm just under the minimum comment reputation, however I have been having exactly the same issue.
Like you, I re-installed Windows 10 (Enterprise) and Visual Studio (both 2013 Pro and 2015 Pro) to no avail.
For the moment, I've put this on the back-burner and am working around it by using a combination of DevArt's Entity Developer (https://www.devart.com/entitydeveloper/) and manually editing the classes to match database changes.
It is tedious, and not a lot of fun - but it works for me (for the moment).
Hopefully this helps someone.
Edit:
For anyone who may come across this post in the future, the following appears to have solved this issue for me:
Though you may not have to, I left "Enable rich client visual experience" unticked.
If this doesn't work, take a look at the comments below this answer - it might be of use. :)
Source: http://pinter.org/?p=2611
Edit 2:
My issue came back, and after further investigation it appears that it was caused by Remote Desktop (I am currently using an ESXi-hosted Windows 10 VM). Switching to VNC or using the VMWare VSphere Web Console results in Visual Studio running perfectly fine. Hopefully this helps someone! :)