Yahoo Search is run through the Yahoo website. It primarily brings you to sources affiliated with Yahoo more than any others. Since they cover so many different topics on their site I got somewhat bogged down when looking at their results page. I would only use it if I used Yahoo Mail as my primary email account.
WolframAlpha is a specialized engine that gives you much more than just "results" to your query. It is a scientific engine that gives you facts to your questions. Calculations to mathematical problems are also a specialty of this site. Not only will it give the numerical answer to a mathematical equation, but also plots on graphs and other forms of the answer that could be needed.