As shabbir and pacman1 pointed out, your PR score has no direct bearing on where you rank in the SERP. Google ranks pages based on relevance, not PR or backlink count.
Backlinks are important but not in the way many folks may think. A backlink ,even from a high PR page, will have no direct ranking benefit if the link is from a page with no relevance toward your targeted keyword. The best way to make your link relevant is to use your keyword in or near the anchortext of the linking anchor. This make the link relevant and it wil then have influence on your pages relevancy score.
Not all backlinks carry the same weight. The ranking power of a backlink is weighted by the PR of the page the link is placed on. This power is then divided by the number of oubound links. So some backlinks have little or no power while others can be very powerful for SEO ranking.
Seek to understand how backlinks can influence your page's relevancy score and you will understand what it takes to outrank your competitor. Bear in mind that proper on-page SEO will reduce the amount of relevant backlink power you will need to overtake your competitor in the SERP.