There are many things considered when we can know why your competitor ranks well than you.
1. Your competitor has more links than you but you are not actually able to see them. How do you know that you have more backlinks.
2. Your competitor has more quality backlinks but you have more in numbers.
3. Toolbar PR of 6 does not have much of importance when it comes too Google ranking but its just self satisfaction. PR is generalized importance and not keyword specific.
4. You have links which targets other Anchor text than what your competitor have them.