I've tried many styles including originals on a wide range of guns, including cartridge guns. I was pretty systematic in attempting to use them as already described for increasing range as well as for leads. Probably reflecting my limitations as a shooter more than the limitations of the sights in those applications, my results weren't so hot. One of the biggest flaws or traps was my tendency in low light or very fast shooting to instinctively use one as an aperture site irrespective of the range involved, which of course threw my shots high. For leads, which were usually needed very quickly, I found them to provide an extra layer of complication in aiming, compared to simply aligning the sights normally and using reference points on the animal for establishing my lead.
Again, that all reflects my own limitations I think rather than an indictment of the sights. Way too many good marksmen over the years have used them as described with great effect for me to be critical. But for my own shooting methods I prefer a primitive sight or a receiver sight.