Chef de cuisine is a "cooking chef". In large hotels the Exec. is (as Anthony Bourdain puts it) a "traffic controller". Mostly logistics, staffing, ordering, and new projects. The Chef de cusine is the flashy cook who wows everyone with his great stuff in the high-end dining room.
Chef de Cuisine usually runs the kitchen of a restaurant when the Exec is over several restaurants or is high profile and doesn't spend much time in the kitchen. Exec Sous would basically be in the same position.
I'm a glorified babysitter...........Yippeeee!!!!!!!