Does AdSense for Search pay less than AdSense for Content?

You're exactly correct that the per-click payment for ads shown as part of AdSense for Search are typically quite a bit lower than AdSense for Content. In fact, I believe it's the case that even if the advertiser were paying the same per-click fee to Google for top placement for a given keyword that the payout to someone hosting those ads are lower.

However, I'm a bit confused by one comment you make: you can't add AdSense for Search to your own pages: you can only specify that you want to include a search subsystem on your site and then have AdSense pages in the search results, as far as I recall. Perhaps that's what you mean?

Anyway, one reason that Search produces lower payouts might be because the page that includes the advertisement is served up by Google itself, while on AdSense for Content the pages are actually part of the Web site (for example, this very page on my Web site, which includes AdSense for Content).

Further, I have to say that I've never made enough on AdSense for Search to pay for a can of soda, let alone any meaningful revenue. If I can quote from my popular book Growing Your Business with Google on this topic:

"The majority of Website owners I've surveyed share that while they might make a respectable revenue stream from the AdSense program, almost none of it is because of AdSense for Search. Your site, your visitors, and your experiences may certainly vary, of course, but while it's important to include a search engine on your site, utilizing one that includes ads might not be in your best interest."

I hope that helps clear up your question regarding AdSense for Content versus AdSense for Search!