Movieclips are good for looping animation and symbols, manipulating it with Actionscript (spawning it onto the stage, and basically doing whatever you need to with code), and it's good for a simple animation that you can get messy with on the main timeline and it will still loop.
Graphics are good for simple animation where you aren't planning on using code. You can set it to Loop animation, play once, or use a still frame from it, without having to code those things with Actionscript. You can also start it on a certain frame. They're good for syncing on the main timeline and manipulating the animation within it. I'd recommend using these if you're not going to code anything.
For example, if you were to use different weapons in a character's hand, you could make 10 different weapon hands inside a graphic and just switch between which frame you want (switch between which weapon you want him to be holding) in the properties window. Or if you want a wheel to spin once then stop, set it to loop for a few frames then enter a new keyframe and set it to Still Frame on the frame it ends on. If you wanted it to play more than once you could loop it and cut it short with a keyframe.
