I have never been to Moosehead Lake so all I can say about it is that people that have been love the area.
My wife and I have been going to Bar Harbor and Acadia NP for many years and we love it there. I could go on for pages but I will try stick to the highlights.
We always stay at Bar Harbor Campground, in fact we are going again next week. ( The Bar Harbor Campground
) It is a no frills campground but they have a nice pool and a nice playground for kids. They do not take reservations and do not take credit cards. They DO take personal checks. You should have no problem getting a site in September after the kids have gone back to school. Some sites have water, electric, sewer (no cable) and many sites are water and electric only. They also have a large number of tent sites, some open some in the trees. They do have excellent free WiFi service. You pick a site, set up, go back to the office and pay. If you want to stay longer just go to the office and pay. Always nice folks working there.
The town of Bar Harbor is a bit "touristy" with lots of small shops but most of Mount Desert Island is sparse, wooded and beautiful. The tiny village of Somesville is one of the prettiest I have ever seen. Don't blink driving through or you will miss it. Notably missing from all of Mount Desert Island are chain stores. No McDonalds, Burger King, Dunkin Donuts and etc. For that you have to drive 8 miles or so off the island to the town of Ellsworth.
Acadia NP is a very rustic natural beauty with both dense woods and fantastic ocean views along the rocky coastline. Highlights of the park are the "Loop Road", Cadillac Mountain (all 1500 feet!), Tea and Popovers on the lawn at the Jordan Pond House and the Carriage Roads which is a network of roads throughout the park for people, horses and bicycles but NO
It seems to us that a week on Mount Desert Island isn't enough time to see it all so we keep going back.
.... and then we go back in early October for the foliage and close the campground on Columbus Day.