Watashi ni Unmei just has better hairstyles and the genders are reversed.
They are practically the same drama, the only difference is STH is way less quieter.
Both movies share the same intensity and atmosphere. Two loners are brought together by something they share in common, but it's the same thing that could easily break them apart. I wouldn't be surprised if Wong Kar Wai took inspiration from Midaregumo.
Both stories revolve around a woman falling in love with her husband's servant and having their love challenged by society.