Though I have used APIs from the companies you have mentioned above, I feel Twitter's engineering team has done a great job with their APIs.
Their APIs are so robust that they have answers for all requirements you will need. Their documentation is very self explanatory and to the point, I didn't like Facebook's developer documentation though.
Not just to mention response times and data correctness and simplicity of their APIs. I sometimes wonder how easily they return data upon such a large data set. The scale with which they work is amazing. Out of billions of tweets, their APIs perform magic by having response times of nearly below 10s (worst case).
There are endless Twitter API wrappers available for every language, I have worked with Twitter4j (For Java) and Twython (For Python) and these wrappers simplify our job even more. It's as simple as it can get. If you have not tried their APIs I highly recommend everyone to give it a shot!
Cheers!