This is totally dependent on the individual and whether you have secondary dysmenorrhea or similar. For many people, menstrual cups have to be changed much less regularly than tampons, so there is less faffing around in your sensitive area.
Some people take a few cycles to get used to the menstrual cup and work out how it works best for them. When a cup is property inserted (and the stem is appropriately trimmed!) you shouldn’t feel the cup inside you at all.
Sometimes the cup doesn’t unfold which might feel uncomfortable – rotating it a couple of times inside you should open it up.
If you have a low cervix or a cervix that moves particularly low during menstruation, the cup may exert pressure on the cervix and cause discomfort and even pain.
You don’t need to wait for your period to start before you can try out your menstrual cup – it’s perfectly OK to do a “dry-run” since menstrual cups wont dry you out in the same way that tampons do.