“I have never used, encourage or endorsed the use of Analytics over web server stats.
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Personally I'm the total opposite
I'm a big fan of Analytics, and with the exception of Google moving to https which screwed up some of the keyword data, I think the combined reporting tools of analytics, adsense, and webmaster tools is powerful, quick, gives you good snapshot visibility and the ability to create customised reporting for your own circumstances.
Parsing server logs trying to get rid of the bot traffic is tedious, and a lot of the data can be very misleading to the inexperienced.
My biggest thing with server logs is the high visitor numbers, which sound great, but paint a false picture. Server logs are supposed to differentiate between human and robot traffic by looking at the useragent, ie are you a human using a browser or a web crawler. But there are now so many crawlers out there, a lot aren't picked up by the user agent.
Coincidently I was having this same chat with a local business who was telling me about the 100's of visitors he gets a day, but was struggling with any conversions. I've offered to help out as a favour, and saw the site had no SEO, page titles were "post1" etc, so doubted the traffic numbers.
Installed GA the other day, and have been comparing against his server logs. Here's yesterdays results, the top is server logs, the bottom from Google Analytics.
So according to his server logs, he has had 266 visits on 27th March.
According to GA, he had 21, of which 19 were unique.
Then there is the old 1990's favourite stat the "hit" which has to be one of the most abused stats ever used in telling people how popular your site is.
Looking at the state of the site, I think I'd believe GA.
Unless I can be convinced otherwise! Personally I'd love a compelling argument that GA stats are rubbish and server stats are accurate, because we base our own numbers on GA. According to our server stats, every house in the UK has visited My Local Services at least once in the last 30 days!
GA also has it's flaws, obviously it's javascript, which may be disabled on your pc, or the code may be at the bottom of the page and not fully load before the visitor clicked away, but if put in the header, and forgetting javascript blockers, I think it gives a pretty good picture.
Back to the OP, the SEOmoz article is a good one, and there is some good stuff in your server logs you can't get from GA, as the examples with the logon page highlighted.
But for day to day health checking, research and running reports, I can't imagine life without GA.
