Most men's cycling shorts use bib straps rather than a waistband, as this can cut into your midriff when hunched over the handlebars. Bib straps avoid this while also keeping the shorts in exactly the right position; there’ll be no slipping about as the ride goes on.
Women's cycling shorts may have straps but often do have a waistband instead, as this makes comfort breaks much easier. There are various ingenious solutions that provide shoulder straps but still mean that you don't have to remove your jersey on rest stops.
Wider bib straps are often more comfortable as narrower ones can cut into your shoulders.