Which is to be used at which time.
In the documentation on http://api.jquery.com/:
For ajaxStop() it says:
Description: Register a h
ajaxComplete is called whenever an ajax request finishes, either successfully or with an error.
ajaxStop is called when all ajax requests complete. So unlike ajaxComplete, it won't be called if there is still a request in progress.
You should use the first if the operation you want to perform should be done for every ajax request.