"More that they have certain problem domains where they might pick a given search engine, and that those problem domains are biased toward using Bing for easy searches and Google for hard ones."

That makes no sense. Why would you, or anyone, alternate with search engines if one of them too often fails to deliver? Why not just use Google all the time and avoid the cognitive overhead?

Does Google do a poor job, or a worse than Bing job, with airplane tickets?