This is interesting.More commonly we hear,“barking dogs never bite,” which at first look is similar as "a dog's bite is worse than his bark." So I googled the later,and found these two expressions are actually opposite in meaning.The former means people who use threatening words usually do not have the guts to do it; the later means people who are quiet may eventually beat the hell out of you.
barking dogs never bite 会叫的狗不会咬人
a dog's bite is worse than his bark 不叫的狗咬人才厉害