I think the second urn is preferable in the repeated case because for really unbalanced ball setups there is a high correlation between the color that gets draw

I think the second urn is preferable in the repeated case because for really unbalanced ball setups there is a high correlation between the color that gets drawn each time. You can just guess that the next ball will be the color that was most common among previous drawings. With the 30/30 red/green urn, on the other hand, you don't really have a much greater edge than 50%, at least in the early phases. In the later phases, perhaps you could count balls to get an edge, unless the balls are put back in the urn after being drawn.