Switching between Chrome Developer Tools and main window full screen
You can use Mission Control (Ctrl+Up) to drag the main Chrome window and the DevTools window to adjacent spaces, if they are not already next to each other. You can use Ctrl+Left and Ctrl+Right to cycle through spaces.

Mac users will generally keep all related spaces adjacent to each other, in a group, and use Ctrl+Left and Ctrl+Right to navigate between them.