I did not noticed such problems with anything except some games. For example, i'm runnin Pillars Of Eternity atm, and if it's running fullscreen mode, i cannot switch to any other apps (i've tried alt-tab, cmd-tab, cmd-arrow, f11, custom spaces-switching shortcuts, touchpad gestures)
Also, in window mode, i can only switch using alt-tab (switching between apps within the same space) if i have other apps running in the same space. Other shortcuts are working only if i'm clicking outside the game.
El Capitan 10.11.6
Best Answer
Have you tried using ctrl-arrow keys? This will move you between the left and right spaces.
A similar question is also here:
How to switch between fullscreen applications in OSX (Mavericks)