I recommend adding events to the MovieClips of interest and not a general handler on the stage that you then sort into different objects. The massive switch statement or whatever that you'd be writing would be annoying to maintain and not really gain you anything.
Indeed, I sometimes put in extra invisible Sprites solely for the purpose of managing which objects have event listeners applied. The reason is because sometimes mouse handlers get confused and behave oddly when you apply a mouse event listener to the child of another object with a mouse event listener; it's cleaner to deal with when all objects with event listeners are on completely separate branches of the display hierarchy.
For example, if I have a button attached to a MovieClip and I want both the button and MovieClip to receive separate mouse events, what I'll do is make an extra sprite and attack both the button and the MovieClip to that.
I want to add the caveat here that it's more efficient for processing if there is only one listener for each event on an object. This is kinda premature optimizations so I wouldn't stress over it too much, but if you have multiple functions that you want to happen in response to an event then it's better to have a single event listener that calls the multiple functions.
This is a slightly different situation than what you asked (a single listener on each of multiple objects vs. multiple listeners on one object) but it's related.