Well FB likes are likely to be of less use than a year or so ago. FB competes with Google for user time. FB has been winning the battle lately and Google does not like that for sure. What are the odds that the "do no evil" company will give large importance to a cmopany they want to destroy? In time they will give very little weight to FB over their own network. The best way to beat giants is to focus on niche topics and have the best content and tools in the world for those topics. If you can grab authority on those topics you can win. We have beaten Amazon on book rankings and Home Depot on tool rankings. It can be done, it just takes focus and time. http://www.activewebgroup.com
If you want to beat out your competitor the first thing you should do is to be able to learn as much from them as possible, this can be through using sites like "compete" which tells you for example, search keywords demographics and things you might find very useful in competing with them, as for facebook fanpages, more fans don't really mean google likes them.