What is the best option?
That depends on what you are looking to get from your Analytics. If you are a looking for more detailed information about the server, the network, and bandwidth usage, then you should look at AWStats or Webalizer. However, if you are more focussed on the business side of your website, number of visitors, visitor behaviour and how to grow your website traffic, Google Analytics gives you much better information regarding the demographics, behaviour and traffic sources of your visitors.
However make no mistake neither of them is perfect, they are both flawed because they do not provide a complete solution. Having said that there is no reason why you cant have your cake and eat it too by use them all. Compare the data collected in each of the technologies, look at where they produce simular data and where they don’t. Also figure out why they are different what the variations are ant you will have another set os data.