Both are lovely. You can’t go wrong. We are fortunate to have friends on both islands who invite us every summer. [ShawWife is generous and charming]. We have more friends on MV and know it better.
We prefer MV. Nantucket does seem a little stuffier. MV friends are more Boston-based and professor types with side businesses (so they can afford homes there) whereas Nantucket people we’ve met tend more towards New York private equity types. Not sure if this is true – sample size is small.
Your life will be a lot simpler if you skip the car and either bicycle or take an uber/lyft (I’ve only used uber/lyft on MV so I’m not sure they exist on Nantucket).
Have a great time.