Larger coils will usually give a bit more depth and of course, more ground coverage. However, they are nearly useless in trashier areas as they try to read too many targets at once and have difficulty sepaprating the goodies from the trash. The weight can become a burden more quickly as well. Supposedly they aren't as sensitive to small items, but I haven't found that to be the case in my own experience. As for fretting about passing things your coil won't pick up, that will always be the case for us treasure hunters unless someone develops a detector that reaches to China. When I first started detecting, I thought that bigger is better (coilwise), but with time and experience, for most of the hunting I do I find the stock and smaller coils much more useful than the larger ones. I do own several for use in conditions that warrant the use of a large coil, however, and It's nice to have the coil options when needed. My two bits.
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