I do sometimes wonder this myself because I have both a Twitter and Facebook page and it's Twitter every time that I get most of my traffic from. Both work just about the same way you have retweet on Twitter and share on Facebook so I don't think that affects it to be honest. I personally sometimes thing it may have something to do with the way they have things set out on Facebook. Not everyone see's a post from a page nowadays since they made changes. I myself have over 60 followers on Facebook and sometimes only 12 of them see my posts from my wall.
Some advertisers may be questioning their investments in paid Facebook ads, but even the brands most unhappy with Facebook's paid advertising offerings are, by and large, continuing to spend big bucks on their Facebook Pages. Those Facebook Pages may not technically be owned media, but Facebook Pages are free, and brands have more control over them than anything else on Facebook, so they're often treated like owned media. But while Facebook Pages are free, acquiring fans isn't and increasingly, brands are looking closely at acquisition costs. So it's probably not good news then that two of the largest search engines -- Google and Bing -- are reportedly driving less 'free' traffic to Facebook Pages.
Its much easier to build on audience on Twitter. On Facebook, people tend to be overly careful when its about adding new people or Liking new pages. On Twitter, the users tend to follow most accounts that interests them.
If you bought most of those 1000 followers, on either network, you're not going to get much traffic from posting anything. Even if they are real people they are paid to follow you and probably aren't even interested in your site.
This is a very valid insight. I haven't thought of this before but it definitely makes sense. I could say that the Facebook community is very active internally. But, yes, very little involvement with outside community.
It could merely be that with Twitter, your tweet ad is integrated right into what your followers see on their profiles; that is, a short and sweet message with a link to your site or some other call to action. It's directly in front of them and more tempting to click than on Facebook where a million different things could be going on at once to divide their attention.
I think the answer for your question lies with the behavior of the facebook community. Many users there use facebook as they'd use twitter. What I mean is, they post every single event in their lives as an invidual post, filling up other people's walls with useless things... And because of this, users began to hide notifications from most of their facebook friends, dealing a huge blow to the flow of information. And twitter also has tags, which make it a lot more easier to present relevant content to people.