Google Analaytics does not "re-count" visitors who return to the site in the same 30 minute window. It also does not count visits from spiders and web crawlers. So in my opinion, it is a much better measure of "unique visits" (of the human kind) than server logs. So while the numbers may appear much lower in GA than in your server logs, they are much more useful from an SEO and usability standpoint.

However, if you are looking to track things like downloads of a particular file or image, then server logs are a must.