Quora has a focus on making questions canonical and reusable, whereas my impression is that Yahoo Answers has a focus on getting answers for users who have asked questions; Some of the reasons that I think this are: Yahoo Answers asks a question asker to choose a best answer to a question which will then mark the question as resolved (which means no new answers are asked for.) On Quora, the person who added the question is deemphasized and other users can edit the text of the question to make it better, and on Quora, the asker of the question isn't necessarily expected to be the best judge of the answers given.
The main reason behind that the people care about the quality of there content on Qoura is that the sole purpose of this site is just for answering the questions and nothing else while for yahoo it have no specifications.
Yahoo questions can be as long as necessary, and can be updated constantly, while answers must be 1000 or less characters. Questions may have details alongside links
Quora questions must be 250 characters or less, and cannot have details, only links. Answers however can be very long, and have pictures, Italics, bold, lists, and sourcing.
Quora and Yahoo Answering, Both are the question and answer sites but most of the users use Quora than Yahoo Answering.
There may be some minor differences between both, But both are used for question & Answering.