One of the reasons I like Asian films and horror specifically is that there is no culture of "the happy ending" which seems to be a western staple.
It's quite ok for the protagonist to die and it happens more often than not
As regards The Ring vs Ringu (Japanese version) I liked the original more than the remake for several reasons;
The 'clues' in the American version were easy to track down (need to find a lighthouse? oh that's easy!) whereas in the Japanese version it wasn't and you were really conscious that time was running out for these people and it was frantic, breakneck pace towards the end of the movie.
The dad. I didn't like it that the father of Sadako was still alive and able to act as a threat. The whole idea of the movie was that the threat was from a source you couldn't defend against or run away from. I felt his presence distracted from that and was 'filler'. It was definitely put in for a western audience so we could see the 'bad guy' get his just desserts.
Anyway, getting back on the broader subject. There's a lot of synergy in asian cinema where they take a western idea and mix it around with their own mythology regarding spirits/ghosts/kami to create something fresh seeming even though you can trace the origin;
The Eye was basically a 're-imagining' of The Eyes of Laura Mars
Audition was Misery+ etc
What helps keep it fresh is that these aren't just remakes but taking the kernel of an idea and then building something original around that. It helps that a lot of the asian stars are not household names in the west so it doesn't suffer from "oh look, Naomi Watts is in danger, but she'll escape because she's a star" syndrome. As we don't really know who's famous enough to escape the chop