"瞧不起" means look down upon somebody or discriminate somebody just as the explanations above。we have another ironic expression about it. It's "狗眼看人低。" Anyway, "瞧不起人" is not a good attitude towards someone else.
"看不惯" means a different opinion about something or somebody. It doesn't include the discrimination about somebody, so it won't cause the other's disgust. In a word, the extent of “看不惯” is lighter than "看不起".