Your sig suggests there'd be 1 adult and 3 kids to pack up and move, making a 1-4 split stay more hassle than it's worth, IMO. It also means the cost of a water park day may be as much as the cost of a room upgrade, depending on the kids' ages. I'd be inclined to stay at CBR for the full trip.
Both CBR & CSR have fun feature pools and beautiful grounds. Both CBR & CSR have multiple bus stops, longish bus rides. But CBR has the Skyliner hub... win!!! Not only do you have faster, easier access to 2 parks, but to all the restaurants at CBR, Pop/AoA, Riviera and World Showcase throughout your stay.
A resort day at CBR sounds awesome to me! With the money saved, you could also take your boys to Fort Wilderness Campground for a horseback ride, bike rentals or kayak rentals - bus to MK then boat to FWC or Skyliner to DHS then bus to FWC. Also consider miniature golf. If the weather doesn't cooperate, go bowling and see a movie in Disney Springs.
Enjoy the other fun things to do on a Disney vacation without the hassle of moving your family on the 2nd day of your vacation. Perhaps on a future trip, you may want to add a deluxe resort day to END of your trip. Stepping up to a deluxe is way better than stepping down, IMO.