A traditional elastic waistband—where the elastic is encased in fabric—is the most common style you'll find on ski underwear. It's simple, secure, and does a fine job keeping your base layers in place during a full day on the mountain. For most riders, it works just fine, especially under looser-fitting ski pants.
The main drawback is that elastic bands can dig in or roll after hours of wearing a ski pants waistband and belt over them. If your ski pants fit snugly through the waist, you might also see a visible line or feel some pressure where the elastic sits. It's not a dealbreaker, but it's worth thinking about if you're prone to sensitivity around your waist.
If comfort under layers is a top priority—especially for women or anyone who finds waistbands irritating—a wide yoga-style band is usually more comfortable. But if you prefer a no-fuss, secure fit and your ski pants have some room through the waist, a standard elastic band gets the job done just fine.