The two ENVI versions primarily differ in the interface. Both are available with the standard installation. The newer version is intended to be more like ArcPro - a single view window, vs the classic view with 3 windows: overview, 1:1, and zoom (typically 4 x). The Band Selection window used in ENVI Classic disappeared.
One of the larger substantive changes is the change in the way Regions of Interest (ROIs) are done - the file format changed for the saved ROIs.
A number of standard techniques that were useful in Classic ENVI seem to have gone away - e.g. in running classifiers, the ability to cross-train on different data sets. If you want to move between IDL & ENVI, it's easier to do in ENVI Classic.
As a practical matter, I find myself toggling between the two versions, but I've been using 'Classic' for a very long time.