In my experience, the sensitivity issue is relevant to the conditions be hunted, just as it is with the smaller coils. True, the volume of matrix under and a larger coil is increased, but it's also the same matrix that's around the smaller coils. If we could freeze the state of this matrix and saltwater/sand then this environment becomes stable and constant and both large and small coils can perform very well. On the other hand, "motion" and "density" become the ultimate deciding factors once this environment begins to move, the ability for any coil to function at peak performance continually reduced as the environment around the coil becomes increasingly unstable. Smaller coils obviously perform better in these conditions because they are dealing with far less instability then the larger coils. This instability is likewise compounded with the larger coils simply because they are harder to control, the stability in their motion also becoming more erratic as the conditions around them begin to provide more turbulence and resistance. So in my experience, the blank statement that larger coils don't perform as well is situational, rather then a standard.
The other factor is density. My area beaches are very fine sand, when compared to other areas of the country one might say that the mineralization density in my hunting environment is very low VS say, Hawaii, which contains a higher volume of mineralization and larger/denser particles. Given the difference in these two environments it is quite possible that a larger coil could easily detect small objects on my area beaches at decent depths and yet completely miss those same small objects on the beaches of Hawaii, this then being compounded further depending on the stability of the surrounding environment.
In the end, big coils can perform very well, but not everywhere and not all the time. Like anything else they are tools to meet certain circumstances and conditions. Sometimes they can do the job well, other times they can't. Just my two cents.
