Answer
The speeds of the two balls are the same just before they hit the ground.
Work Step by Step
The speeds of the two balls are the same when they hit the ground.
The ball that is thrown upward slows down until it reaches maximum height where the velocity is zero. The ball then falls back down and accelerates downward as it falls. When this ball reaches the starting height at the balcony, the ball's velocity has the same magnitude $v_i$, but now it is moving downward instead of upward. Therefore, the speeds of the two balls will be the same just before they hit the ground.
