Basically, they are two different things, and they work just like jackets do.
If you put a synthetic jacket on over a down jacket it makes you warmer - assuming the down isn't squashed flat because the overjacket is too tight.
If you put a Goretex jacket on over down it keeps the down dry.
It's the same thing with sleeping bags. An overbag is like putting another puffy on. A bivy sack is like putting an uninsulated hardshell on.
If you have a down sleeping bag, do you want to make it warmer or do you want to make it waterproof?
If warmer, use an overbag.
If waterproof, use a synthetic overbag.
If both, use both.
You can dry out a slightly damp down bag in otherwise dry conditions by putting an overbag over it because the warmth of your body and the way you move the dew point outwards will make some of the moisture move outwards away from the down bag into the synth. You can't do this just with a bivi sack.
On the other hand a synth overbag by itself over down in wet conditions (dripping wet snow cave, rain, or even sleeping directly on snow) is not waterproof enough to prevent your down bag from getting wet and becoming useless. First the synth will get wet, then it will make the down wet, then you will be screwed.
I hope this answers some of your questions.