Recently there was a discussion about CIWS in the sci.military.naval newsgroup. I'm now trying to give you a short summary. Hope you enjoy it.
There are two totally different systems: the gatling gun systems (Goalkeeper, Phalanx) and
the missile system (RAM).
A problem of the gun systems is the kinetic energy. A 1000lb missile moving at 300-350m/s isn't going to be significantly affected by a half-pound projectile moving at 1000-1500m/s in the opposite direction. The problem is that, with Phalanx tyimagesally scoring its kills by warhead detonation at 500-800 metres, if the warhead survives there's a good chance that the missile - even with its seeker shredded by 20mm APDS - is on a ballistic trajectory intersecting the ship. (One reason for the replacement of 20mm AAA with 40mm and 3" guns in the Pacific late in WW2 - by the time 20mm was in range, a kamikaze was likely to hit the ship anyway). RAM is doing much better. It can blow the rest of the inbound missile out of the flight profile.
Also evasive manoevres greatly complicate defensive fire, especially using guns.
note: I've got all these informations from the usenet! If anything is wrong don't blame me.
I've to thank all the people who were interested in the discussion and wrote something.
Maybe I'll later write a table version also.