Could be either. Depends in large part what YOU do with it. If there is 'potential' and an 'unofficial site' hustles and does a really good job of offering information, SEO.....then being official won't mean much - because another site is doing a better job, getting better buzz, and eventually outranking yours.
Also depends partly on what you are the official site for. Are they going to be providing PR support, exclusive or first access to key content.....? It should eventually come to be that you are doing them more of a favor than you are doing them. Depending on what you are the 'official site' of and what the agreed terms are, I would built the site to be highly and quickly convertible.
You do have an actual, agreement of some sort I hope. What would it take to be stripped of 'official' status. What is the expiry of the arrangement? Renewal options for both sides? You could build a site that is worthless if getting locked out of the ability to use the content and/or 'official' connection.
Why are you the official site? If they 'need' you, that could be a win-win deal. I would consider the need to design the site with a built-in parachute - where you do not need them for the relevance of the site to survive and continue despite whatever comes up. Something will, always does.
Nothing that I am involved with would benefit from an 'official site'. It would be better if more competitors went away or quit trying to keep up with us. LOL