Not particularly scientific but here is my attempt at comparing results from Google and Bing (using this rather useful side-by-side tool http://www.blackdog.ie/google-bing/search.php).

I’m based in the UK and the results went to the .com site (as opposed to .co.uk so it’s not clear what impact this might have. I’ve selected five searches which seem fairly reasonable terms.
I’ve also included the URLs so you can better see where the results are from.

Search term: prostate cancer screening

Google top 5

Bing top 5

Verdict – A marginal win for Google, Bing returned results that were slightly less focussed (e.g. the general Wikipedia article on prostate cancer or slightly less reputable.

Search term: MMR autism

Google top 5

Bing top 5

Verdict – A clear win for Bing. A controversial topic and it returned the most robust sources.

Search term: type 2 diabetes metformin

Google top 5

Bing top 5

Verdict – Clear win for Google. I felt the results were more focussed using Google.

Search term: side effects statins

Google top 5

Bing top 5

Verdict – A draw, I wasn’t really impressed with either (half a point each)

Search term: acne

Google top 5

Bing top 5

Verdict – A win for Bing.

Overall verdict is – rather boringly – a draw with two ‘wins’ each and the rather disappointing draw. Given that Bing is so new (2 days old) I think it’s pretty remarkable!

NOTE: See techcrunch’s none health comparison: Search Smackdown: Bing Vs. Google