They might try the query on Bing, fail, and then try the same query on Google. A large portion of those are likely to fail as well, just because the queries are hard.
It's less likely that someone will try a query on Google, fail, and then think "Maybe Bing will do a better job with this."
It would cause Google to have a relatively larger proportion of "difficult" searches. Many "difficult" searches on Bing will be repeated on Google, but not the reverse.
If you assume that all "difficult" searches fail on both engines as a first approximation, that would mean that Google will fail all the "difficult" searches, while Bing will only fail the "difficult" searches made by people who primarily use Bing.
It's less likely that someone will try a query on Google, fail, and then think "Maybe Bing will do a better job with this."