...say that u got robbed or some "unfair" incident has happened and u want ppl to know about this. i saw ppl post their stories online and drastically their tweets get retweeted so the local ppl spread the fact
Ok, think about that for a second. How does that happen? It happens because they have a circle of friends who know friends, and a tweet can go viral. For a local incident though, you may as well stick to Facebook or another social media. You have your friends in the area who can react.
When you first made the post I was thinking of a more global impact from a tweet. You can publicly tweet, but someone in Egypt (it sprung to mind given the recent revolution) isn't going to care if your paper got stolen and you want to catch the perpertrator.
Twitter, like any social media, can have a range of impact. But it depends on what you're saying. For your particular situation - or at least, for the examples you provided - you would get just as good a response posting such things to Facebook as you would posting it to Twitter.
I think of Twitter like this: A medium to send minute-by-minute updates on current affairs. That's how I used it, and others use it differently. But a majority of the tweets that are publicly available could easily be reduced to a person's Facebook update, where their circle of friends will read and react while the rest of the world doesn't care.