Yahoo! Search Builder
There are some differences between the two that make them fairly unique. Yet both, for the site specific searches, require that your site has been indexed fully for it to pull any relevent information.
One of the differences on Yahoo! Search Builder is not being able to have any ad's personalized as from AdSense.
Two nice things from Yahoo! are the ability to manage the "search in" location and that you are able to track the performance of the search box. You can specifically set the search location to be the web, a specific web site, or a mixute of both, as well as dis-allowing specific words in a "Most Popular" section.