Well to answer the OP's question; I tend to judge films purely on their merit, not on the basis of being a remake or a sequel. (Judging films on their merit gets me into a lot of heated debates, when I insist that an adaptation of a novel was a good film in its own right, whereas someone else insists that since it wasn't rigidly faithful to the novel it automatically becomes a bad movie).
So for the three "J Horror" (god I hate that phrase for some reason) films:
I saw Ringu before I saw The Ring and much preferred the original.
I saw Ju-On before I saw The Grudge and I thought that they were both reasonably good, with neither one having much over the other (I think The Grudge was paced and plotted better, and was more cohesive as a film, but this reflects Ju-On's origins as being destined for a TV series).
I saw Dark Water but haven't seen the remake. Didn't think much of it to be honest. What was presumably supposed to be tension and foreboding just felt slowly paced, boring and wiht not much of a pay off.
(I included which order I saw these films because I think that this can affect your judgement; if you see two film that a very similar, the first one of them you see might appear to be groundbreaking, fresh and new, where as the second one you see might just appear as "same ol', same ol'", regardless of which one is the original and which the remake)
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