This is entirely situational because target speed is factored in before the cap. It works if the turret and fire control are as fast or faster than the target, but the 100's still give better PD performance against faster ASMs due to reduced leakage.
Sorry for taking so long to reply.
The thing is that missiles are almost always faster than the fire-controls of point defence even at slightly lower missile versus PD tech. So whether you use a 100% or 50% from that perspective might matter somewhat.
Although, in practice it does not really matter if you have a smaller gun or a larger one from a leakage point of view, the difference is so small and depend more on how many fire-controls you have rather than size of the gun so you don't waste shots as much on overkill on salvos. Putting large 100% Gauss in quad turret might be a waste against low salvo numbers, such as from fighters for example. You also presume scenarios that almost never exist such as one salvo of the PD will be able to take out all the missiles on one salvo, this scenario will rarely happen in practice.
Smaller guns also can get some additional effect from having more barrels per turret and are cheaper to research, both the gun and the turrets. Smaller turrets also give you more leeway of designing stuff in the same sense that smaller engines does. I think that turrets will be even more effective in terms of efficiency in C# too. The tracking bonus might also make smaller Gauss way more effective if you can increase the tracking of the weapon closer to the speed of the missiles.
So over all there are many benefits to using smaller Gauss guns that has nothing to do with the minuscule lower efficiency of a 100% or a 50% gun. The combination with ASM being both slightly larger and slower will probably also effect PD choices to some extent.
Also... you should consider that having missiles leak through the PD can also be a strategy in and of itself. So having some missiles leak through and hitting your shields is a good way to know you are being effective with your use of AMM and PD efforts. If the extremely small difference in leakage between a 100% gun and 50% is noticeable then you PD fire are so effective it does not matter anyway.
I am factoring per fire control so fire control count is irrelevant.
Two shots at 50% cth has the same average hit rate as one shot at 100%. Against one incoming missile the single will kill it every time while the twins will both miss it 1/4 of the time. Against two incoming missiles the single will kill one and miss one every time while the double will kill both 1/4 of the time, one 1/2 of the time, and will miss both 1/4 of the time. In both cases the twin has a 25% chance of missing completely and a 6.25% of doing it twice in a row. In the two missile case that means more than doubling the minimum shield requirements, while in the single missile case it means needing shields at all. This is not a 'minuscule' loss of efficiency.
If that was all there was to it there would be little point in ever fielding the smaller cannons, but cth modifiers exist and must be taken into account. As I have not yet tested the Fighter Combat Bonus, I will focus on capital ship defence. Crew grade improves cth without affecting tonnage, and better than 100% effective cth is wasted. Grade is subject to a training cap at 35% so anything more requires taking combat damage. All other modifiers are penalties.
Taking into account modifiers against a given target, a smaller weapon with an effective 100% cth will always be superior to a larger weapon due to higher hits/tonne, and a weapon with less than 100% cth will always be superior to a smaller weapon due to less leakage. There is a tradeoff between a weapon with a greater than 100% cth and a smaller weapon with less as the smaller weapon will have a higher base average hits/tonne but will also leak.
With a 0% grade bonus and a 95% fire control, a Gauss-100 will not exceed 95% acc against any target and will leak slightly. Smaller weapons will leak more with no benefit.
With a 35% grade bonus and a 95% fire control, a Gauss-67 will have 83% cth against same speed and slower targets, an Gauss-85 will have a 100% cth against targets with a 9% speed advantage, and a Gauss-100 can match a 28% speed advantage. Against anything faster the Gauss-100 will always give the best performance but will still leak.
With a 35% grade and a 74% fire control, a Gauss-100 will have just under 100% cth against same speed and slower targets.
For C# Aurora and assuming the tracking bonus is a multiplier like grade is, a 40% tracking bonus, 35% grade bonus, and 95% fire control, would let a Gauss-100 match a 79% speed advantage, a Gauss-85 match a 52% speed advantage, and a Gauss-67 match a 20% speed advantage.