It is pretty much equal. Using Hyannis as a central location it is 74 miles from Logan - Boston, google maps puts it at 1 hour 24 minutes; 83 miles from TF Green Providence, 1 hour 33 minutes. A lot depends on when you will be landing at either airport in terms of traffic you might have to deal with. You can also fly Cape Air from Baltimore to Hyannis - you can take the train from DC to the Baltimore airport.
just to clarify - you will need a car once on the Cape so even if you choose Cape Air plan on renting one.
I have found that the car rental rates are becoming really pricey. You might want to get some car reservations first then, based on that, choose Providence or Boston. Providence is smaller with less hub bub and, last time I was there, the cars were parked right outside of baggage claim. If you fly into Hyannis I have found that Enterprise is still somewhat reasonable especially at that airport. Good luck.
Even when my kids were small, we usually drove to our NE vacations. Mainly because, packing was easier. Flying requires getting kids into and out of car, thru security, waiting to board plane, hour ride, waiting for luggage, getting rental, then finishing drive to Cape. It is about a 5-6 hour drive to Providence.
It is about that much time to get there from time you leave your home until you are on the road in RI.
But, PVD is the easier airport to navigate if you are not familiar with Boston. Traffic will depend on time of day and day of week for the balance of the trip.
Your vacation won't start until you arrive at your lodging, unpack, and pop that first beer.
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