First, the assumption is that you are saying you have a page that is ranking for the term Blue Applesauce but it is ranking below the Red Applesauce page when searching on Blue Applesauce.
There are a lot of factors that can go into this: recency of content of one over the other, links to red applesauce may be stronger or more prevalent, the poorly ranking page may need to adjust on page SEO, etc. Also, while the readable content on the page may be the same, does one have better markup than the other, get more traffic, etc.
There is no one answer and certainly no one cause. Look at the content understanding that when you know your pages very well, sometimes you "miss the forest for the trees." So, have someone else go over it to see if they see it differently. Also, be clear that not all keywords are the same... So ensure the query you are using is very specific to what you want to find in search results. Adding any modifier like cold, great, tasty, etc. can impact which page ranks for Blue Applesauce based on the content and on page seo.
Now, if you are speaking about you have a page and are being outranked by a less relevant page that is someone else' you have opened an entirely different discussion: beyond the issues above, this one pulls in the subjective idea of what is relevant issue.
I hope this assists you to some degree.
Robert
) If you choose a company from the US, I would look for someone on SEOmoz as well.