I had seen the American remake some time ago, but had never seen the original. After hearing how it had revived the horror scene, not only in Japan but in America (how would we have ever gotten the "majesty" of Pulse without it?), I was a little surprised to find I liked the remake more.
The cliche is that American remakes always add more - more explosions, more gore, more tits, more monkeys, more whatever - and end up with less. Here, somehow Gore Verbinski (a little while before going Pirate crazy) managed to add more and end up with more. The cursed video tape is a bit creepier - and is utilized better to drive the investigation. The effects are more - instead of just having a Dalek-like reversed image to show someone buying the farm, we get a really creepy twisted face effect. And instead of the fairly simple background story for the little girl (Sadako in the original, Samara in the remake), we get a little more meat in her effect on the island's inhabitants. This pays off in the creepy horse suicide scene on the ferry later.
Also, the lead character Reiko also gets less to do here than Naomi Watts' Rachel character. In Ringu, Reiko is aided by her ex-husband, who happens to be psychic. Most of the information the two learn come from his grabbing hold of someone and doing a Christopher-Walken-in-The-Dead-Zone impersonation. She's mainly along for the ride until the end. In the remake, her son is the psychic, and he gives out a lot less information. Instead, Rachel has to rely on good old-fashioned investigatory skills.
Still, both films know how to do the slow burn. Once the pieces start coming together as the seven days click by, the tension starts to mount. And having the big reveal occur at the bottom of a creepy well was an outstanding choice - what a horrible way to go for the little girl. Of course, the standout scene is the final attack by Samara/Sadako, and both films do an outstanding job. It's by far the most effective scene here, and brings things to an effective bang before the somewhat anticlimactic ending. Three stars.