I have heard great things about Awstat but have been loyal to google since they have over 50% of the Search Engine Market Share. Google Anaytics is so easy to use and very informative so why would someone want to use awstat?
Personal opinion I suppose... some people don't like Google knowing everything that they are doing. Plus it is a good idea not to run your landing pages on the same stats network as your PPC ads because it is a lot easier for them to inflate their numbers and charge you more.
Both are good, but depends what stats are important for you. I mean google stats are more marketing related...