VS2012 could open up VS2010 projects and leave them in a state where they would be usable in VS2010.
Does VS2013 have the same feature?
If you allow Visual Studio to upgrade the project automatically, you can open it in Visual Studio 2013, Visual Studio 2012, and Visual Studio 2010 SP1.
from following link
http://msdn.microsoft.com/en-us/library/vstudio/hh266747(v=vs.120).aspx