Both are outstanding schools, so there is probably no wrong choice.
Yes, Dartmouth has a strong Greek life presence, but more than half of the students are not in fraternities or sororities, so please don’t feel like you will need to join one to have friends, have a social life, fit in, etc. I know students who are very happy at Dartmouth and are not in fraternities or sororities. People I have come across from there are generally friendly.
I feel like Dartmouth’s culture/vibe is a little more laid back than Williams. And I mean that relatively speaking, because obviously you will have rigorous academics at both.