Subtitles. I’ve only seen one movie where the dubbing didn’t detract from my enjoyment of the film…but I umm, can’t remember the name of it.
Nitpick, CTHD was in Mandarin. But I know exactly what you mean, and love a lot of kung fu and anime. There is very occaisionally a quality dub that happens, it is nice but very rare. I’ve been watching the anime Chobits on YouTube, and am very surprised at how good and well-performed the English dub is.
Many of Michelle Yeoh’s movies, including CTHD, she did the additional English overdub herself. So watching the dub you don’t miss out on her wonderfully beautiful voice 
Jackie Chan has also started doing the English dubs of his HK movies also, but his command of English isn’t strong or fluent enough to really deliver the emotion as convincingly.