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If you already have another TeX distribution (like MacTeX-2015), it is not necessary to remove that distribution before installing MacTeX-2016. The old distribution will remain after installation and you can easily switch back to it if you discover a flaw in TeX Live 2016.
To change the active distribution, run TeX Live Utility in /Applications/TeX. In the Configure menu, select Reconfigure Distributions. A small window listing available TeX distributions will appear. Select the one you want to active. This click automatically reconfigures all TeX GUI applications, and automatically reconfigures the PATH and MANPATH variables. See the documentation on Multiple TeX Distributions for details.
This feature is not available in the version of TeX Live Utility installed on Leopard machines. See the documentation on Multiple TeX Distributions for an alternate method available on Leopard.
If you want to remove your old distribution after installing MacTeX-2016, read the document on "Uninstalling".
For a list of new features in MacTeX-2016, click here.