I want to know if there is any keyboard shortcut to switch between splits screen in all new El Capitan.
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.
I really hope someone has a better answer, but if not, Command+Tab works if the two last apps you've touched are the two apps being splitscreened.
It is possible
For Google Chrome for macOS users:
Hit Control + F4 to go the right screen.
Hit Control + Shift + F4 to go to the left screen.