I don't think Bing is as good as Google, no other search engine in the world can compete with Google, at least when it comes to content in English. Google can almost read my mind, I can't say the same about competing search engines.
If the last web site you visited was for the Audubon Society and the next thing you search for is Cardinals you will get a page about birds on the first result, but if you had just recently looked for tickets to a ball game on Ticketmaster you will get the baseball team as your first result.
One of the more fascinating things that DDG's "Dontbubbleme" campaign did, was expose just how big a swing in the results your 'meta data' has. People who are running Chrome and are "logged into Google" get very different results than people who make a query with no context following them around.
In the latter case everyone has to resort to giving you the pages that "most" people clicked on from your geographic region [1].
Bing and Google have pretty much exact equivalence if you remove tracking and geo context. (IP blind / cookie blind / search).
[1] For even more fun, set up proxy servers in various data centers around the country and do searches with no cookies or context, and proxied to different geographies. Very enlightening.