I wonder where you have checked the page rank of your website and competitors website. Google has stopped showing PR few years ago and there is no way any tools/person can get actual PR of a page.
I am not saying PR is redundant. PR is very important for any website and its still one of the most valued ranking factor. So, you need not be worry about the Page rank of your website and for competitors as well. Google's algorithms for Page rank still works the same way they used to works years ago but nobody will know the actual PR of a page.
Now let me answer your question. Page rank (ranging from NA, 0, ...to 10) algorithms works in a way where all the links plays an important role. Wherever your page has a link on any web-page, it will get a certain value from that. For example if your abc is linked on efg and efg has a PR of 4 and there are 10 links in total on efg then 4/10 value will be assigned to each pages who have a link on efg.
So in simple words try to get links from better PR pages which don't have much links on it. But as I said earlier that you cant have actual PR of any web page, so try to get links from highly relevant and great information rich pages and you'll be fine.
Hope this post answer your question.
It's not easy to improve how you rank against your competition, but there are some best practices and strategies you can put into place.
I have a few on my site: nerddigital.com.
Feel free to reach out to me there and I'd be glad to review your site with you.