It is almost like the debate "Which came first: Egg or Chicken?" Facebook and twitter both have significant number of users. They both are popular and effective for website promotion. Though Facebook has the largest number of users, you can not say it is the best to promote a website. So, I would choose both.
I made use of Facebook because i believe it has more visitors online daily than that of twitter. In addition one can get targeted traffic by buying ads in terms of country and niche unlike twitter. i have tried it out and it worked for my page, i now get likes continuously on a daily basis.
If you are looking to choose just one then more information will really help people make some informed and informative replies for you. Things like what niche you might be targeting, what your target audience is, what exactly your website is about as well as any other important information will greatly help you to get the answers that might best suit your needs.
What works for one person and their website/s will not always work for all websites. I have gotten better results using Twitter for promotions but I also use Facebook and some others depending on who I am looking to attract.
If you are looking for ease of use then Twitter is a good choice as it's simple and to the point but again, it will depend on many factors.
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