I rarely use either one and have perfectly healthy teeth and gums. I believe in cleaning from the inside rather than the outside. A diet, like one rich in fruits and veggies, that rids the body of toxins and supplies nutrients to your gums and teeth so they can fight off disease all on their own.
I prefer mouthwash, it makes my mouth feel cleaner! I use it every time I brush.
I always use mouth wash. I never saw salt as an option but will need to try that sometime see if it makes a difference.
Salt in a glass of water for gargling has been effective in temporarily easing pain in sore throats. Finding the culprit is still necessary, like is it a bacterial infection causing tonsillitis? So direct and correct treatment can be given.