I want to set it up so that I can use the same keys for both - so if I am moving between spaces in OSX and get to fullscreen tmux, it starts switch through tmux windows, and if there are no more tmux windows then goes to the next space.
Not sure if you can have something like that map to the same key combination. The default behavior is Ctrl + arrow [left | right] to move between spaces and you tmux prefix key (default : Ctrl + b) and [p|n] for previous and next.
I'm not sure how to change the Mac shortcut to use Ctrl + b + [p|n] for moving through spaces, but changing your key prefix in tmux to just Ctrl to get the Ctrl arrow mappings might mess with other shortcuts.