For most skiers hitting the resort, 4 buckles are the way to go. They're the industry standard for alpine skiing because they give you the most precise, adjustable closure across your foot and lower leg. Each buckle controls a different zone, so you can fine-tune the fit—snug where you need it, relaxed where you don't.
The big advantage is power transfer. With 4 buckles securing your foot and ankle evenly, less energy is lost between your leg and the ski. That means quicker edge-to-edge transitions and more responsive control, whether you're carving groomers, hitting the park, or charging through crud.
You'll see 3-buckle or even 2-buckle boots in the touring world, where saving weight and speeding up transitions matters more than maximum downhill performance. But for any resort skiing, sacrificing buckles just saves a few ounces at the cost of real control. Stick with 4.