It's often hard to do away with personal bias when evaluating the quality of search results across different search engines - you may be more familiar with the interface of a particular engine, which skews your perception of what is genuinely most relevant, or you may just like seeing your own sites and pages in the top spot. Of course, relevance can be defined somewhat more strictly than that - but it's always a matter of taste.
Enter the search engine blind taste test, by someone called Michael Kordahi:
It allows you to view results from each of the "big three" search engines - but without knowing which is which. Note that the author is a Microsoft employee, and hence has a vested interest in steering people away from the overwhelming brand in the search marketplace (Google). And of course, the recent rebrand of Microsoft's Live search engine as "Bing" is likely an added incentive. In the online marketing community there were a lot of positive comments about relevancy in Bing results - which surprised me, as much of the same community slammed the results when the same algorithm was framed as "Live" ;)
In any case, the test itself is valid enough, and you might be surprised at the results. Head over to Blind Search and see for yourself.