Hatebreed are metalcore. They are about 50% metal / 50% hardcore.
Hardcore is a style of punk. As soon as the guitars play in that Swedish melododeath style, the band ceases to be hardcore and becomes metalcore, a style of metal.
KSE are not metalcore. I have seen them live, along with Shadows Fall, and I would definitely compare these bands to each other. Neither are hardcore OR nu metal, yet they get called as such by completely ignorant metalheads (a word which should be synonymous with moron) who claim that any metal band that they don't like is nu metal.
KSE is mostly melodic death with thrash and hardcore influence.
Shadows Fall is thrash with death and hardcore influences.