At least Adsense is guaranteed income once clicked, whereas a Google search will end in no revenue unless an ad is clicked from the new search.
Adsense always pays me, the search box only shows one or 2 sponsored results and then normal listings, there is a huge chance that they won't click on a sponsored ad.
That not necessarily true. If users do a site search, there is a good chance they will find something on your site, spend more time on your site and end up clicking on an ad eventually. A site search ads stickiness. Has anyone every done a comparison of number of pages/visitor with and without site search. It might be worth looking into.
Perhaps by having the Google Search feature, it will make your site look like it's completely sponsored by Google, so then the Ads by Gooooogle text above adsense ads won't make the ads look so much like ads? Just a thought.
wow that much you must tell me your secret as i am doing less than that. I took it off a forum i run and after a month a thread was started with loads of replies "can we have the google search tool back" just like last time i have loads of searches but very little CTR on the ads. I think a lot of forum mebers dont like change and see the search box as a comfort blanket rather than a tool.