If you go into the subgenres of metal and punk, you can find plenty of things that aren't "loud". Metal and punk are far too broad to really just cover by themselves, you essentially have to go into subgenres or else you're being too vague.
Personally, I'm more of a fan of post-hardcore, gothic metal and power metal, as subgenres, but I like a lot of the heavier stuff and some skramz.
Favourite bands that fit the genre, for me, include Silverstein, Parkway Drive, All That Remains, Epica, Ice Nine Kills, Kamelot, Draconian, Altaria and The Devil Wears Prada.
So yeah, to expand on the earlier point, there's enough variety that someone will like something in the genre. If not, they're probably deaf.