Budget-wise, I'd pick Monos... sure, it's a hassle packing all the groceries, etc. for your trip, but transportation and of course, feeding yourself is cheaper than the same, for a trip to Tobago.
The accomodation in either place depends on your budget, but if you factor in your savings on transportation and food, you could probably afford a nicer place for your family, 'down the islands' than in Tobago, on the same budget.
That said, the seabathing is far better in Tobago. Also, if you'd rather hotel services like housekeeping and prepared meals, Monos would not be the choice for you.
I would go to Tobago. If it is vacation then I would at least want to get away from familiar surroundings. Additionally, I dread that trip through the Maracas Mountains as it seems to have become unsafe and a hassle in itself because of the number of cars that frequent there. Usually I would only go to a place like Monas with five or more people, which means the stay is short, in Tobago I would be there at least for a couple of days.