You two guys are going to be head to toe for a while til you:

1. Match his authority
2. Get more "votes" links of authority than him

Match Authority:
1a. Find where his links are coming from and dup them plus a little more. The higher PR and authority...the better.

1b. Match his market reach then expand it for yourself. If he's Marketing through forums for an example. Make your presence there as well. If he has publications out in the target market...then do the same plus a little more.

2a. Find he's linking structure and dup it plus a little more. If he does hubpages, then you should too.

2b. Contact him and do a banner swap...etc.

2c. Offer to exchange quest posts.

2d. If he is setup to where he allows comments on his blog. You should do that too.

Use SEOmoz's Open Site Explorer tool to help execute some of debra's suggestion.

I've been able to outrank many competitors who have used the competed keyword as their domain name. What I can really suggest is to build "trust" (though it will really take time). What I'm pertaining about trust includes the following:

- frequency of links built along the process
- link landscape (naturalize the look of the off page optimization with regards to the amount of nofollow and dofollow links built)
- anchor text variations that includes the main keyword
- quality and age of the links built (best if you can have highly relevant links that your competitor doesn't have, given that your competitor has lesser backlinks, you can surely have an advantage with this)

Just be patient and wait. Also, it's important that you include disclosure/disclaimer/privacy policy pages on your site, these can help your site get more trust scores from search engines.

Just build more links, write better content and find another avenue for traffic. Eventually you'll over take him.

Depending on the age of your domain that could be it. If his domain is say 2 or 3 years and yours is only 1 then that may just be it. The ratio may be putting you lower in the algorithm no matter how many links and whatnot you have. As others have said in time yours will be on top if you really are putting in as much work as it seems you are.

To outrank such a site, just build a massive backlinks by doing the following:

1. blog commenting

2. High PR profile links

3. article directory submission

4. social bookmarking

5. RSS submission

If you are jumping up and down on page one then Google has not really decided if you even really belong as the number two site. This means that you are quite a ways away from overtaking the number one spot. Increase your seo efforts and you should see that you can lock in the number two spot.

If your competitor is an exact match domain, you only should make more backlinks for your website to dominate it. Because you can't so any other thing except on-page and off-page factors and if the on-page factors of your website are well, you should concentrate on off-page factors and backlinking is very important for it.

You need to build and distribute content according to your keyword as third level back links ips will effect on the ranking.

Quality and high PR backlinks, backlinks, and backlinks.

I am still surprised so many people are so focused on link buying. There are much better ways to rank site now days.

Exact match domains have an initial bonus given to them by Google. Only way to outrank them is to build more backlinks or find an Exact Match Domain yourself.

Some people suggest over 200 elements are considered in calculating page rank.

Certainly, many report that domain age holds weight - as does the projected length of stability. When is your competitors domain set to expire/up for renewal, and when is your's?

Consider expanding your approach to a more targeted niche approach - building key phrase content targeted to a narrower market.

Certainly quality rank is impacted by quality backlinks. What efforts have you expended to build your rank already?

Regards,
Melanie

I would keep building links and keep producing content. Make sure you are doing it all at a faster rate then the guy in the number 1 spot and eventually you should take the spot.