Hi James,
I (and others) have answered this a number of times recently so I'm mainly going to link you in.
http://www.seomoz.org/q/how-does-this-site-rank-higher-than-a-seemingly-better-one
http://www.seomoz.org/q/can-t-for-the-life-of-me-figure-out-how-this-is-possible-any-ideas
http://www.seomoz.org/q/why-would-a-site-with-virtually-no-external-links-and-low-authority-rank-very-high
The basics of it are you are looking at maybe 3 or 4 metrics of maybe 200 that affect SEO. DA and PA matter but they are heavily influenced by other factors such as domain age, page loading speed, time left on registration (surprisingly!), number and quality of anchor text vs branded text, follow vs. nofollow (not in the ways you'd necessarily expect), and again, like 175 other factors. There are always a million "could be" answers.
Let's say the other site had a PR7 SEO site before and it is now offline. Maybe they used it for the "black hat" version of their business. They've seen the light, black hat works less than ever, and they've gone all white hat. Now they 301 that domain over to the new one. You can't "see" the 301 but the effect would be massive. Maybe they have one big client who they managed to ask for and get a big link that isn't on the Moz index but it's showing up in WMT. Maybe their average visitor visits 3 times as many pages as on your site or stays for 10 minutes longer per visit. Those type of metrics make a huge difference in SEO.
I hope that helps answer your question! A huge amount of factors control SEO - social, possibly, the platform of the site, +1s on Google, local citations that may not include a live link so they aren't picked up by Moz.... see the issue in figuring this out?
~Matt