As a general rule of thumb I always read/experienced myself that about 14" in max physical coil size in a DD was the limit in terms of still gaining depth on coin/ring sized targets. About 10.5 to 12" for a concentric in that respect too, in general, as DDs tend to hold onto small target sensitivity better as they increase in coil size. There comes a point where the size of a DD or concentric starts giving less depth on coin/ring sized targets. Bigger is not always better in that respect.
But, the other major factor as to max coil size for gains in coin/ring sized depths is the minerals you are in. In that case, I found the 15x12 did not get as good of depth as my stock 10" coil in my mineralized soils, and often gave better depth for it's self if I lowered sensitivity a good bit lower than what was max stable. Just sucking up too much ground stew I would think when ran too hot. Even the official field test of this coil shows at dime/sub-dimed target sizes the 12x10 takes the lead in depth. The 15x12 was a half inch or so deeper on say half dollar sized targets or bigger, which one would expect.
In my soil around a 12 to perhaps 13" coil size is the max in a DD to still see gains in depth on coin/ring sized targets. DDs also ride on my soils/sands better and give me more depth over a concentric due to a DDs smaller view of the ground matrix. Not even sure if a round 12" coil is not too big for gains in depth in my soils. The 12x10 is the deepest coil I ever used in my soil due to it's rather sharp focused less "fuzzy" field I would suspect, while another 12" round DD coil doesn't seem to get the same depths for me in comparison.
The 13" Ultimate might be the rule breaker though, and I suspect due to it's unique design that seems very different from "conventional" round DDs by both the looks of it and also it's traits in the field. I don't think it's deeper than the 12x10 in my soils or sands, but it might be as deep. Still contrasting that when I replace the loaner I had with one of my own to sit along side my 12x10. The 12x10 is my coil of choice for stability, depth, and fantastic left/right separation, but I do like the Ultimate for coverage in very large areas I want to grid faster, although the 12x10 is still a nice improvement in that respect over my stock 10" coil. The Ultimate may be big, but it's weight is lighter, like the 12x10, than my stock 10" coil on my machine. Won't wear me out in long grid searches in big open areas of fields or beaches.
While, depending on soil/sand types, the 15x12 might be borderline for some one way or the other on depth gains for coin/ring sized targets, for sure that 18x15 is well beyond the realm of that and is meant more for a cache or large relic coil, or for large area coverage where that is primary on coin/ring sized targets and depth is secondary.