Think of 12 people you know but are not friends with. Not bad people just not your friends. Would you want someone to randomly choose one of them to decide your fate or let all of them discuss it? I'd rather have a group talk about it and decide together. Choose the one wrong person and you could be in trouble regardless of the problem.
In my opinion I would say having a jury is much better than letting the judge decide because with a jury many minds will try to reason together. You also avoid cases of biasness since a judge might pass the wrong judgment because of his/her personal feelings towards you.