They are different vibes. They all have wealth in different ways and so many of these so called "comparisons" are just off. The Hamptons is more for New Yorkers who are used to Manhattan all the time and get out to nature, exclusive beaches, towns with upscale restaurants, etc. You often have to drive to the beach and they don't mind. It has an unapologetic happening "scene" at night. They are more focused on being luxurious and glamorous versus "charming". People take themselves seriously.
Nantucket/ MV has the classic New England vibe- more family oriented, historical buildings and hydrangeas, bike rides to get ice cream in your sear suckered clothing. Nantucket has one town versus MV has several with different personalities. Edgartown is the preppiest and most like Nantucket. MV has older homes, lots of diversity and some crunchy/hippie vibes in some areas. Don't go for a glam scene for either- there isn't one especially in MV.
Lots of daytime activities- beaches, biking, boating but I wouldn't go alone or think to meet anyone
