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 think both saltwater and mouth wash work, however, I would think that saltwater would be less effective as it's not specifically designed for rinsing the mouth.
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.