Don't know what you mean by limited, but logfile-based analytics software doesn't have access to as much data as software that can use other data sources like cookies (ie it has difficulty tracking sessions).

If I might ask, why exactly do you need to make your analytics completely undetectable to users? In most cases tracking pixels and the like have no effect whatsoever on the user experience.

Also, are such systems limited, compared to Javascript or PHP based tracking?

Yes. Javascript enabled tracking gives you a lot of additional information. For example: screen resolution, plugins, which link was clicked on a page to get to another page (not referer - the actual link).

It's also possible to track a user's mouse movements on a page (which can give you heatmaps of usage on a page)

Cookie based tracking can show if a user has visited the site previously, and track particular users throughout the site, perhaps over multiple visits.

Most log-based analytics tools cannot filter out bot traffic as well as a JavaScript tool would. Additionally you would be missing other information that could be obtained from JavaScript like supported Flash versions, screen resolution, etc.