Re: voltage drop
A 200 amp panel will seldom have 200 amps worth of load running on it. You can certainly design it to have no more than 3% VD with a load of 200 amps. But if you do, you may end up with a larger feeder than is needed. That is a design (and economic) choice, not a code issue. But then, VD is not a code issue either.
I agree with sky1's calculation of a 4/0. But if the load were actually, let us say, 160 amps, then a 3/0 would be adequate.