Although I love Nantucket, I'm an infrequent visitor, so I don't profess to be any sort of expert. That said, assuming that you mean the town center when you refer to "Nantucket" (I believe the whole island is actually a single town, Nantucket), the biggest difference between there and 'Sconset is that in town you can walk to a large number of restaurants, bars, and shops, whereas there's very little commercial development in 'Sconset--one restaurant and one small general store that I can conjure up out of memory. Staying in town, you might realistically be able to do without a car. I wouldn't want to do that for two weeks in 'Sconset.
In my opinion, 'Sconset is an exceptionally enchanting corner of an enchanting island, and I think I'd be inclined in that direction, other things being equal or at least comparable.
Last two weeks of June could be hot, warm, or cold weather, dry or totally drenched in rain. The water temp, regardless, will be cold (in fact it typically only 'warms up' in Aug/Sep and, even then, it isn't bathtub water). So, staying near downtown (meaning historic downtown Nantucket where there are stores, restaurants, ferry dock, etc) vs. on the beach (lots of locations..if you look at vrbo you will get a good gander at the possibilities and price ranges from simple capes to manses but you'll probably want to use a realtor if it's your first trip), is probably the better bet.
That said, I have friends who have, for the past 40 years, rented all of June on a remote beach...specifically because they like to sea kayak, cook, read, write and be left alone; they seldom go downtown.
If the prices of lodging, dining and so forth are off-putting once you do your research you can still visit Cape Cod. Nantucket is the most expensive option you can choose in this area but, hey maybe you'll run into super rich John Kerry wind surfing when he has some time off from being Sec. of State. There is a lot of variety of accommodations and restaurants and scenery on the Cape itself if you want to consider it.
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