Why the golden ratio is better than the rule of thirds

Well neither rule is better or worse than the other, both are simply guidlines of composition. A simple way of comparing the two is the the of third is set out in a grid divided into even thirds (33/33/33) the golden ratio is approximately a 62/38 division, the golden ratio leads to the intersection of important diagonals. 

When composing there is nothing to say you can't use both in the same image, there is more than likely a built in rule of thirds grid in most dslr cameras. However, the golden ratio is a little harder to use.