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It's just luck/RNG. The chances of ring drops on the final boss is the same in either dungeon.
In addition to a drop chance on the final boss, the first mini-boss of CoH2 has a chance of dropping a named healthy ring, the lich boss of CoH1 has a chance of dropping a named healthy necklace, and the penultimate boss of CoH1 has a chance of dropping a named arcane necklace.
Using that website you can find the set you want to farm and see where it drops and if there are any unique drops which have a greater drop chance. So that you can farm it easier. For instance you'll notice that there is a ring and a neck that is a unique drop. So youd want to farm that particular boss until you get your piece.
From the looks of it COH2 for rings (Dropped by: Ibelgast) and the neck youd farm COH1. (Dogas the Berserker for arcane neck and Uulkar Bonehand for healthy neck)
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