I have heard that some people earn more money with twitter.I don't know about the real fact but I can suggest you that by making your site interesting can earn a lot of money.
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sponsoredtweets is good for the earning money but you have to post best tweets and tweets are going on the moderation and after it shows on your account.
I prefer Twitter is the most popular for the business and social networking. Twitter have best performance with the compare of Face book. You can check its page rank which is provided by Google.You will find Twitter's Page Rank 10 and Facebook Page rank 9. so Twitter is good.
So far, I used twitter for sharing any interesting facts about my niche and also new blogpost. Yes, I agree with our friends those using twitter to gain more traffics to their sites.
I don't know how many people like Twitter. Some one express their opinion that it is difficult to earn money with Twitter. I believe that none is impossible for man. So, you can also earn money with Twitter by taking some steps such as: sharing interesting facts, doing as SEO service, setting more followers, promoting your site and so on.