You can indeed install both versions side-by-side. In fact, Visual Studio is designed such that you can install not only different editions within the same version (e.g., VS 2013 for Desktop alongside VS 2013 for Web), but also different versions (e.g., a VS 2013 edition alongside a VS 2015 edition).
Check out the Installing Visual Studio Versions Side-by-Side article on MSDN. The only stipulation that Microsoft makes is that versions should be installed in the order in which they were released (e.g., install VS 2013 before VS 2015 products).
On my personal development machine, I have VS 2012 Desktop, 2013 Desktop, and VS 2015 for Web installed without any issues whatsoever. I routinely run different versions at the same time as well.
Asked in February 2016Viewed 1,634 timesVoted 7Answered 2 times