The number one rule of SEO is that search engines rank web pages, not websites. So you need to compare individual pages, not entire websites if you want to understand why you are being outranked.
One of the disadvantages of a WordPress blog is that the default configuration will constantly change the home page content. While this is good for fresh content it makes it a bit tougher to maintain a consistent ranking position. You can resolve this by configuring your blog to use a static home page.
By now I’m sure that you have heard that search engines don’t rank you by the number of backlinks, your experience is yet more evidence of this fact. This is a myth that is promulgated mostly by folks selling backlink services based on the number of backlinks they create. Many backlinks are completely worthless and some are very powerful, so a simple count of backlinks tells you very little. You have to assess the power of each individual backlink to accurately analyze your competitor’s backlink strength.
Search engines rank web pages based on relevance, not the quality of content. Backlinks will only help you rank if your backlinks increase your relevancy score for your targeted keyword. This is why relevant backlinks are essential for highly competitive keywords.
Don’t confuse relevant backlinks with backlinks from related topics websites, those are two different subjects. Again the #1 rule of SEO applies: Search engines rank web pages, not websites. It’s the relevance of the page and especially the anchor text of your backlink that makes your backlink relevant. The website topic is mostly irrelevant.
To summarize the answers to your questions:
Search Engines Don’t:
- Rank websites (they rank web pages)
- Rank pages based on the number of backlinks
- Treat all backlinks the same
- Rank based on the quality of content
- Allow irrelevant backlinks to influence Ranking
- Use the website topic to determine the relevance of backlinks
- Rank based on the amount of content on the page
Search Engines Do:
- Rank web pages (not websites)
- Rank pages based on relevance
- Value backlinks based on the relevance of anchor text and page content
- Weight backlink value based on PR
- Allow backlinks to influence page relevancy
- Allow outbound links to influence page relevancy