The difference between tracking and opening fire between the two will be far more then several seconds. The Phalanx spins up in seconds (very few) to full rotation. In that picture you have a two barrel 40mm. One third the firepower capacity of the Phalanx and nowhere near as fast however larger in size. As far as tracking and opening fire the older retired system is to say for lack of a better word retarted compared to those two radars and the CIWS can travers 85 degrees plus in seconds. Those mechanical mounts were a mix of electric and hydraulic and more then likely water cooled to maintain barrel integrity. If they are within range of the two it is not even a contest compared to the modern Phalanx system. I have been first hand privy to some of their capabilities from the men that operate those systems today. That information need not be posted here. Obviously you give those systems very little credit as compared to the older mechanical systems whose systems are dependent upon radar systems that were not their own and located some distance from the mounts where as the CIWS systems are fully dependent upon their own onboard system with the back up of other ships radar systems to feed them targeting data.
If compared on the very same plane, they are not comparable. In the space of time it would take the mechanical 40 mm to engage, track, lead and then fire 100 rounds the Phalanx could more then likely let go several 100 round bursts easily and much different then the 40mm instead of leading they are auto correcting mid stream because of those radars. IMO, there is no comparrison if both are operating within the very same parameters. The 40mm has bigger shells, the CIWS hands down will fire slew rates faster with more accuracy and with a stiffer penetrater then the 40mm would ever posess. That is only because they are very scarcely used with exception to the Spectre's and Spooky gun ships that employ them even today.
On one hand the 40mm is a bigger projectile (twice the Phalanx) on the other the Phalanx is faster (firing and reacting) and can put far more penetrating steel in the air faster and more accurately the the antiquated 40mm system.
Couple that with the FLIR system attached to the updated systems and no plane with its heat source (especially a WWII kamikazi) will escape the Phalanx once in range. And yes the new systems can easily track slow moving objects as well. These guns have also shot down mortars in Iraq, they are a proven system.
I did not mean this to become a comaprrison of these two systems. Orginally it was CIWS vs. Kamikazi,