Great question! There are tons of differences between menstrual cups and tampons.
One of the biggest differences between menstrual cups and tampons is the absorbency. Tampons absorb moist from the vagina, even though the periods might be very light. Menstrual cups won't disturb the natural flora and pH at all. With menstrual cup you won't create any trash (you'll get zero waste periods!) and you'll also save a lot of money.
We've written a blog article about the differences between tampons and menstrual cups! I believe you'll find it very interesting!
The article can be found here: https://www.lunette.com/blogs/news/game-on-menstrual-cup-vs-tampons