I've been quite pleased with out stats - that is, once I got the hang of it.
Here's what I figure: Look at Pageviews as your actual hits. What it considers a hit is any file access at all. View one page with 10 images and you've got 11 hits.
Also, if anyone references an image from your site on theirs, that is a hit everytime it loads.
I like them a lot because it shows a LOT of detail that is confusing at first, but once you get the hang of it you will know which search engines give you the most hits, what files are more popular, who's stealing images from your server, and if you look hard enough, you can even see every visitors search string that they used to find you in a search engine. I use that a lot, it helps find your better keywords, etc.
That was a ramble. Anyway, personally I like the stats as they are, but if you want to use another program, it may want the logs to be in a particular format - every server is different. With Apache, you can set it up to log many different parameters.
Oh, now that I think about it, right now there is no client domain being logges - I wonder if the log files are half with and half without client domains? Could be that Fast stats can't read it because it's not consistent... just a guess.
Hope this helps.