With significant air resistance, the ball thrown straight down will strike the ground at greater speed.
Work Step by Step
Consider the ball thrown upward. When air resistance cannot be neglected, on the way up, the ball loses more speed each second than if there were no air, and does not rise as far. On the way straight down, air resistance decreases the magnitude of the acceleration and the ball gains less speed each second than if there were no air. The conclusion is that the ball thrown straight upward returns to its starting point moving more slowly than its initial speed, i.e., more slowly than the downward-tossed ball. Therefore, the ball tossed downward will hit the ground below with a greater speed.