keywords in domain name gives an unfair advantage
have yo checked the quality of the backlinks? 1 backlink from a PR7 related website is way better than 1000 PR0 backlinks from unrelated websites

For me when I look at it in the SERPS my results are reversed. What you have listed as three actually ranks as two.

When trying to analyze your competition consider all the factors, both on page and off page. For off page factors consider number of links to that page, anchor text of those links, and the page rank of the pages you are competing against.

I like the SEO Quake Plugin for Firefox, gives lots of good info.

since the keyphrase "overcoming panic attacks" is not that competitive, you can either outrank other sites' ranking either by adding more content using those keyphrases on every pages or getting more backlinks from other sites. Looking at how overcomingpanicattacks dot net did it, it has tightly themed pages which Google love plus the occurrence of the keywords on each of the pages definitely outranks the other site.

how often keywords are mentioned on the pages ranking in google for both sites

keywords / overcomingpanicattacks.net / other site

overcoming panic attacks / 3 / 0
overcoming / 4 / 0
panic / 24 / 8
attacks / 21 / 0

Inbound links or same site links for both sites

keywords / overcomingpanicattacks.net / other site

overcoming panic attacks / 2 / 0
overcoming / 3 / 0
panic / 21 / 0
attacks / 19 / 0