Hrm, yeh, I wasn't very clear with my criteria in evaluating... The best I can say is that I think they are better.

Searching the web is a science of heuristics, not algorithms. There's no way to prove a result is correct, because there isn't a mathematical way to say something is "relevant" to something else.

Because no one can prove a search result is correct, and that Google has basically been the best search engine for nearly the past decade, the best I can say is that these search engines are as good as Google. Take the list of results from Google, and compare them to the list generated from AlltheWeb or Windows Live/Amazon A9: they're pretty similar. This is not a good method for comparison but is the best I can come up with.

Whether you think a "relevant" or "best"result is near the top is a little subjective--I could say the same about AlltheWeb or Windows Live. I also find order of results not so important, because I almost always have to end up going through all the hits of the first page, not necessarily the first few.

You neglected to mention features and UI. Like I mentioned in the article, for some reason I like Amazon S9's and AlltheWeb's UIs better than Google's. AlltheWeb's LiveSearch is up there on the most interactive search engine UIs I've ever seen, much better than anything I've seen from Google.

So, basically, they're not Google, and that I think they are better, is enough reason for me to use them.