Interesting question! It turns out that the ball would reach the ground first, while the magnet would be slowed down by the coil.
What happens is as follows: As the magnet passes through the coil with some speed on its way down, it induces a current in the coil, making the coil behave like a magnet that repels the original magnet. This phenomenon is termed "Lenz's law", which states that "an induced current is always in such a direction as to oppose the motion or change causing it".
In this case, while the magnet is entering the coil, it induces a current in the coil. The coil tries to resist the increase in current by repelling the magnet. Thus, there is an opposing force on the magnet which slows the magnet down. Then, when the magnet is leaving the coil, the coil induces a current to, again, slow the magnet from leaving it. We can think of the coil itself as a magnet which repels the entering magnet and attracts the departing magnet. The ball, in contrast, experiences no such "drag force", so it reaches the ground first.
If we replace the coil by a long conducting tube, the effect would be amazingly apparent, as shown in this video: http://www.youtube.com/watch?v=sPLawCXvKmg. As the magnet falls through the conducting tube, each circular cross section of the tube acts just like a coil as the magnet passes through it - a current is induced around the tube to oppose the motion of the magnet.
Hope this helps!
References: Lenz's Law in Wikipedia http://en.wikipedia.org/wiki/Lenz's_law
(published on 04/19/11)