Tim Bray just posted some of his experiences in building a web search engine, and how people use simple vs. advanced search.
It's a good (and short) read. I've noticed a similar pattern of usage, although I don't have any form of statistics to back it up. Looking through the logs in CAREO, hardly anyone uses the advanced search page. I think I've only really used it while building/testing it... Simple search does everything I need.