I vote for Yahoo Answers. They are more popular, and they give more information. Some of the answers are usually copied and pasted, but there are still experts in each topic so you will have at least one answer that will solve your problem. I've seen many answers off-topic to the actual question in ChaCha which is mostly why I wouldn't recommend it.
I would say Yahoo Answers. There appears to be more users on Yahoo Answers and I notice that a lot of long tail keywords turn up Yahoo Answers more than it does for ChaCha. If you establish yourself as an expert in one of those fields on Yahoo Answers, you can expect a lot of people to visit your own website. I would recommend answering about 100 questions, and then start using your webpage as a "Source" page below each of your answers. People will start coming to your site and recommending it to others, even years down the line.
I would use Yahoo answers because they rank higher in Google search engines than ChaCha. I read that Yahoo answers is listed second only to Wikipedia for information and answers. It takes time to build up enough points so that your link is clickable, but it is worth it in my opinion.
To be perfectly honest with you, if I were to market something smartly, I would probably use a culmination of both Yahoo Answers and ChaCha. With Yahoo Answers, it is easy for your answer to be flagged if you aren't careful about the phrasing and content of the ones you post, regardless of your level, although a higher level will tend to discourage sabotaging people from flagging them. On the other hand, like the users above me have said, the site ranks much higher and is vastly more popular than ChaCha, meaning that the effort you put into posting your links may garner a much better return on traffic in any period of time. Also, Yahoo Answers is very community oriented, meaning it is indeed possible to establish your site as an authority on a particular topic or niche, whereas it may not be as possible with ChaCha. Unless you were to, say, comment the same link on a variety of the same type of questions. The risk of getting flagged is greater with this, however.
I wouldn't shun ChaCha altogether, though, as people tend to post some very targeted questions there for a random visitor to find, too.
All in all, the clear winner is Yahoo Answers as the best traffic source.
If I were looking for an answer, I'd probably choose Yahoo! Answers instead. It seems to be a bigger community, so in return, you get a lot more responses. I don't have much experience with ChaCha, but I've been on it while browsing a few times, and it seems a bit smaller. I also feel like ChaCha is mostly Googled facts and info as opposed to Yahoo! Answers where people share their personal experiences.
I think Yahoo Answers is better than ChaCha, I tend to always Google search a question I may have at times, and I always find myself on Yahoo Answers to see what people are saying about the question I have. Yahoo Answers is very helpful. I also agree with above posts.
I have never used ChaCha, so my answer might not be fair. Yahoo Answers is ok for bring some traffic. From my observation, it can bring in the most traffic when the question is still on the first page in its category. Once the question is moved to the second page, the traffic goes way down. From that point on, unless the question somehow appears on the first page of the Google search for its keywords, you won't get much traffic from there at all.
I had never heard of ChaCha prior to reading this thread. However I will certainly check the site out now. I was a regular contributor to Yahoo Answers, providing mostly answers to questions. I liked using it. I found it a fun way to help others. I have contributed to Yahoo Answers for like 2 or 3 years and subsequently stopped because at that time I noticed some contributors not taking things seriously and providing wrong or really off-topic 'trying to be hilariously funny answers'. That basically is why I left. However after having read about it here, I might give it a go again!
Yahoo answers. I think it its a much more simple and more used website. Everyone has heard of it, everyone uses it, and theres a reason for that. You usually get pretty quick responses to any questions on there as well, so it definitely gets my vote.