Snap and zip fly closures make the most sense if you're shopping for baggy mountain bike shorts, commuter pants, or casual cycling pants. They give you a secure, familiar feel—just like regular pants—so you can easily take them on and off, which is handy if you're stopping for coffee or running errands on your commute.
The tradeoff is bulk. That snap or button can press into your stomach when you're leaned over the handlebars, especially on road bikes with a more aggressive riding position. If you're doing longer rides or road cycling, this can get uncomfortable pretty quickly.
For mountain biking and casual riding where you're sitting more upright, it's usually not an issue. Just keep in mind that if waistband discomfort has bothered you before, you might be happier with a wide comfort waistband—or even switching to bib shorts, which skip the waistband problem entirely.