Yahoo doesn't really have a search engine, and hasn't for five years. They resell Bing and add some in-house content. The only reason to search with Yahoo is if you want their in-house content.
Bing is currently more literal-minded than Google. Google is using too much popularity-based machine learning to "correct" what you're searching for. It's become difficult on Google to search for a non-popular thing that happens to be close to a popular search target. Google does not treat quote marks as a mandatory exact match any more, just a hint.
Running a search engine is so profitable that even the little guys with < 1% market share make money - Ask, InfoSeek, DuckDuckGo, and Blekko are all profitable. (Cuil blew it - no revenue model.) The most valuable ads on the Internet are the ones on search results, because they appear when someone is actively seeking something. Almost all other ads are interruptions. The only thing that keeps the phone vendors and carriers from entering the search engine business is huge payments from Apple, Google, and Bing.
Microsoft's current approach to Bing is unusual. Bing used to have its own CEO; the last one was Satya Nadella, who is now CEO of Microsoft. Now, various parts of Bing are under five different Microsoft VPs who also have other responsibilities. Some people speculated that this was in preparation for closing down or selling off Bing, but that doesn't seem to be happening. Anyone know more about that?