Since I've done this before for a couple other search engines, here's a side-by-side Bing vs Google comparator.  

I haven't tried enough things to have a very considered opinion, but here are the first few tests that went into my preliminary unimpressedness with Bing:  

kate bush covers
president twice
president obama's birthday
thread query language
where the rose is sown
capital of estonia
boston to asheville
36 jfk street
austin population
primitons reissue
ellen barkin buckaroo banzai picture  

[11 June note: this post itself is now (temporarily?) towards the top of Google's results for some of these terms! But not Bing's. Good demonstration of the observer effect, at least.]