Why give all your searches to one search engine and one company?
Depending on what you're searching for, Google doesn't always provide the best results.
Compare the results for queries like "that movie where a computer plays tic tac toe" A very reasonable search if you forget what the name of War Games is, but bing fails it utterly and completely; not a single mention of War Games until the second results page, and the wikipedia page for it doesn't appear until the third. Meanwhile on google the first results page barely has anything that isn't about War Games.
Now, if you just search "War Games" both will do fine. For that matter, so does Wikipedia's builtin search...
You can push it even further and get more vague, something like "that car that james may goes fast in" and while at that point google starts to degrade, it still easily beats out bing.
Suppose I am looking for "that movie with a button". Yup, google get's it, "The Box". Bing thinks I am thinking of Benjamin Button, which was google's second suggestion (I wasn't). Fair enough though, suppose I actually had been thinking about "that movie where the guy get's younger". Both google and bing don't do great, though google still definitively does better.
Hm. There is no one google. In the google that I see, for that search, it's the other way around: "Benjamin Button" is #1, and "The Box" is #2 (both on IMDB).
Life before search engines was different and it's easy to be blasé. IMHO, getting the one that you are vaguely thinking of anywhere in the top 5 is a great and amazing technical feat. And also good enough to jog your memory, so #1 or #2 makes no difference.