Keyboard shortcut to switch screens on split view
Here is another partial solution. If you split your screen between two windows of the same program, e.g. Safari, then Cmd+` (backtick) will toggle between the two.

Caveats and Special Cases:


If for some reason this does not work, you probably don't have this shortcut enabled. The answer at https://superuser.com/a/187072 explains how to do this.
This was tested on High Sierra, but should work just the same on El Capitan, and so on.