I have had success moving my site for important key phrases in a very competitive field to the top 40, but how do I get into the top 10 when I am up against sites that have been around longer and have more man power?
Focus on the quality of your backlinks, not just quantity. A good quality link is worth thousands of worthless links. Keep your content fresh and updated. Fresh content helps increase your site's credibility and Google loves fresh content. Also, look at your onsite optimization. Is your site built with messy code? If so, cleaning up the code may help you rank higher. Sounds like you have been successful - sometimes it takes a lot of patience. Keep doing what you have been doing and wait for a while. You may see further improvement.
First of all, you will need patience to break into the top-10 for competitive phrases. That and a lot of hard work producing quality content while getting quality backlinks from related sites.
if you wanna catch up with them, then find out what they do. do it yourself and then some. first, analyze their site for title, description, keyword density, domain name, backlinks, etc. then incorporate that to your site. once you have done all the onpage optimization, focus on link building and see where they get backlinks from. get as many backlinks you can from where they get their backlinks from and you yourself keep getting related backlinks yourself at the same time. don;t go crazy getting backlinks and work on it slowly but steadily. it might take some time but it will work out
First, focus on your content Second, optimize your html, metas and stuff Third, install google analytics and try to get conclussions from the metrics, like where your visitors come from, what keywords use to find you Fourth, compare the data with what are using your competitors and tune your site according to the conclusions