Both are mystery/thriller/suspense shows with both female leads being able to see/sense spirits who is accompanied with a supernatural detective whether he is death himself, the grim reaper (black) or a simple detective who died and came back as a spirit (the ghost detective) if you like mystery/supernatural then these are the shows for you.
scary super fast zombies who will tear you apart. one depicts a modern apocalypse and the other depicts a historical apocalypse. both will definitely keep you on the edge of your seat.
Both pioneered the whole "america remaking asian horror" films in the early 2000s and both are about a vengeful female spirit set out on attacking anyone who crosses them. if you've seen the american version of either films you need to watch the original. they're so much better.