Well I don't know nagios, but I do know awstats and webalizer.\\
They both spit plenty of data, but I think it's well organized. Maybe awstats has too much things, but I guess that most of them are self explanatory and you can extract valuable information from some of the information, like for example:

* If your visits are going up (always a good sign)
* What's your most viewed pages
* The 404 your server is issuing.

But since I never had to analyze awstats for a server that has for example 10000 hits a day, I don't actually have the feel of doing such work. Although I do believe that in such cases it might be difficult to process data...Maybe if you keep you head clear, restrict the working set to just the top 10-20 lines of each table that display relevant info you might get along (or not).