This seems to be the ever-lasting question. Before the answer was quite obvious and simple, being that you should choose a studded tyres if you wanted a good winter tyre. However, big advancements in the development of the non-studded tyres have made them so much better than they used to be. Nowadays the question is not that easy to answer. Now it depends a lot more of your preference and where you live and what the conditions that area has.
The studded tyres are still a bit better on ice and tightly packed snow, but the difference is small. The non-studded tyres also perform well on ice nowadays. They use the addition of grip crystals to the tread that increases the traction between the tyre and the ice. They also use a design in the tread that allows the rubber tread to bite into the ice and create traction. If you are not in need of the absolute best grip on ice, then a non-studded tyre gives you a bit more flexibility as there are less regulations on non-studded tyres. If you travel by car between different countries, then you are probably best by having non-studded tyres.