There is no problem moving projects from VS 2013 to VS 2015. Here is an excerpt from Microsoft's website:
"Many widely used assets behave the same in Visual Studio 2015, Visual Studio 2013 and the two earlier versions. For example, in Visual Studio 2015, you can open a project that was created in Visual Studio 2013 or Visual Studio 2012, change it, and then reopen it in Visual Studio 2015; your changes persist and the project behaves the same as it does in the earlier version. The same is true for many assets that were created in Visual Studio 2010 SP1.
If you use Visual Studio 2015 together with Visual Studio 2013,Visual Studio 2012 or Visual Studio 2010 SP1, you can create and modify projects and files in any of the versions. You can transfer projects and files among the versions as long as you don't add features that are not supported by one of the versions."
Hope this helps.