Not being able to see your domain and that of your competitors makes answering this question with specifics a bit challenging, but SEOmoz defines PA and DA as predicting a page or domain's ranking potential in the search engines based on an algorithmic combination of all link metrics.
That said (or defined) I would surmise that you have good links, just not as many as your competitors, and your competitors probably have more than a few strong links from domains with authority (in both PageRank and Trust). Check out the image below. It shows a client's site (top) and five competitors. While it doesn't reflect your situation of a higher DA , it really demonstrates the effects of quality and quantity.
We have the most external links, but with fewer root domains than competitor two, and that domain's have a higher DA to PA ratio for the top five links than we do (90/28 vs. 70/60)
Definitely use the SEOmoz Competitive Link Comparison in your campaign vis-à-vis your competitors
Our global link popularity metric, calculated in a similar fashion to Google's PageRank (on a log scale between 1-10).