The main difference is that server logfiles track all server activity from browser based surfing through to Googlebot visits and non HTML file downloads (such as images viewed via Google images),  analysis of those gives a picture of both real AND automated visits. Client-side scripts only count data for browsers used by real people viewing HTML pages and therefore give the most accurate picture.

Generally, most people want to know which is the best tool to quote for online advertising purposes or for analysis of real visitor browsing behaviour. To do that correctly you really have to turn to a client-side tracking application like Google Analytics, this ensures that the spiders and robots are discounted, cutting page view data reported by log files by around 30% (in my experience) and affecting session time (although I’ve not figured out whether it inflates or deflates it yet as who knows how long a crawler stays on a site each day – possibly just seconds, or once a month for 20 minutes).

Digital ad servers like Doubleclick, which themselves use client-side code to serve adverts, will produce ad impression data which excludes automated crawlers – this is why Google Analytics data will usually be quite accurate for selling advertising. There’s not really much point in giving the outside world a false view of how busy a website is from logfile analysis if their expectations on ad delivery will be dashed when a campaign is initiated.

With that in mind it is sensible to take around 30% off of logfile sourced page impression and visitor data. 30% is my average, I’ve seen some sites with a 15% discrepancy and some with 45%, hence I play it safe at around half way.