One of the biggest differences (for me) is that instances of
MovieClips can have names, but Graphics don't. So that means if you
are going to use code to change the visibility or move it around
you will need to use a MovieClip.
The next difference is that a MovieClip's timeline plays
independently of the timeline it is on, but a graphics timeline
does not. To see this make yourself a nice little MovieClip (or
graphic) animation. Something easy like a ball moving across the
stage or so. Put that animation on the main timeline and make sure
the main timeline has only one frame. When you try it with the
animation as a MovieClip it will play, even though there is only
one frame on the timeline. That is because the movieclip's timeline
plays independent of the timeline it is on.
Change the clip to a graphic (you can do this with the drop
down panel or you can make a whole nother clip, your choice). When
you try the same experiment you will see that the graphic doesn't
play. That is because it is not independent of the main timeline.
If you extend the main timeline a few frames (keep it shorter than
the length of your animation) you will see that as a graphic the
animation will start to play and then jump back to the start. But a
movieclip will just keep playing.
So any time want something to play regardless of the timeline
it is on you will need a MovieClip. Anytime you want something to
play in sync with the timeline it is on you will want to use a
So for frame/hand drawn animation you will most likey want to
use graphics. That way you can keep different parts of the
animation in sync.