Personally, I think the lactic (traditional) method is better than the quick method. Part of the problem with the quick method is that it fails for incredibly vague reasons. So you'll be there with your cheese and it won't stretch, but you won't have any idea why. The vast majority of people fail to make quick mozzarella. Sometimes (because the planets are aligned) it just works and if it does, it's not difficult. But if it doesn't you're left staring at a blob of unstretchy cheese (at best).
The traditional method is how real mozzarella producers make mozzarella cheese. You have control over the process because you can test the cheese periodically to see if it is ready to stretch. However, it is *still* a very tricky cheese to make. If you are a beginner, I highly recommend trying several different kinds of cheese first before attempting mozzarella. This will allow you to get an understanding of the process and what everything is supposed to look like.