ohhh i was always wondering why the french used crotale but no gun CIWS and yeah thats what i was thinking with the phalanx but i never knew about water cooling very interesting insight. How does a system like the Millennium gun compare would it be like in between phalanx and dardo with a low rate of fire compared to phalanx though (burst mode may add an advantage though) and for a system like the 76mm does the low rate of fire leave it at a serious disadvantage or the range is so much greater it makes up for it
The OTO 76 is actually considered CIWS/Anti-ASM capable. This is why Italian ships have so damn many of them.
The big advantage of "big gun" CIWS (40mm-76mm) is that they're "triple-purpose" - they can engage sea and land targets in addition to missile and air targets. So if you're looking to maximize economy they're the weapon of choice. Once again this is why Italian ships tend to be bristling with guns compared to their other nations' counterparts in order to get adequate coverage. This starts to eat into your economy and defeat the purpose, as far as tonnage goes (especially as these are comparatively heavy and have massive deck penetration to begin with). You can get away with, say, a 76mm at each end (and that's considered quite considerable anti-surface firepower) but at the expense of coverage. You also get a heavier explosive shell and the RoF isn't as low as you might think, but these "big gun" CIWS systems are unproven in an actual combat situation as far as actual missile/aircraft shootdown situations are concerned and the RoF is still slow enough that you're betting on the accuracy of your systems to take out the target within the first few hits.
TimothyC already went over Goalkeeper and Phalanx. The Millennium Gun is something of a Super-Goalkeeper: same firepower, somewhat less deck penetration and now you get at least some of that "dual purpose" use as I described from the above. MG is probably a bit better at actually engaging small surface craft than Goalkeeper and that's what MG's primary purpose is for anyway.
The biggest advantage of missiles is that since they actually lock onto and home in on the target you have a much greater pK (or at least in theory). You also have a much longer engagement range - the whole impetus was because the engagement range for Phalanx is so short the ship would still suffer significant damage from flaming debris resulting from missile detonation.