The reason is simple - Twitter module does a lot more than provide a Twitter block. It allows you to post directly to Twitter from your Drupal site. Just note that to use Twitter module as a Twitter block, you will need to install and activate Views and Views UI module.
It may seem like complicating things, but if you need flexibility and reliablity of a large team of Open Source enthusiasts, you should opt for the one that gets more effort put into.
You may not notice any change on my homepage sidebar, but I have shifted to using the Twitter module and it looks as my custom module with minimal change to the CSS. (I just changed the class to id supplied by the View).
Perhaps, I will write some basic documentation of what I got using the Twitter module.