Yea, I know. What I meant is that Google isn't browser sniffing. If you search using Firefox and enter the search terms in Google's search box on the page itself, the results will be the same as any other browser. But if you do a search using Firefox's built in search bar, then the client=xx is added. So this would be Firefox modifying the URL, not Google.
Why the number of results is different, though, I don't know. The adult filter was the best theory yet but that was disproven.