Color coat stucco vs paint on stucco

So I can see light at the end of the tunnel on my house addition. Thanks for all your opinions @ptiemann, @jil ,@maluka and others.
From the last time I posted, things have been going much better. I threatened my contractor with legal action and he has since been delivering good work at much better velocity. I have about a month to go before I am done.

Now I have a question about stucco. The stucco guy did an initial scratch coat on the addition, and will come back to do the 2nd coat (brown coat?). He says thats all he will do. However when I do some reading I find that it is possible to do 3 coats - a 3rd color coat. So, what is the difference between putting on a stucco color coat vs putting on an explicit exterior paint on stucco ? Which is better long-term?

Also I am having one brown coat of stucco put on the rest of the house - too many cracks and patches to be fixed - and this looked like the best way. How will this layer go on ? Will the paint have to be scraped out first and then the stucco put on ? I am trying to learn so that I can be certain about the quality of work.