We just got back from five nights at BC (hotel room, not
DVC) and stayed the same week in 2017 at the Poly. (Not DVC). We were with four kids ages 3 to 8. I vote for Poly. Our kids' fave parks were MK and AK both for the daring kids who liked thrills and the less daring kids who preferred the "cute" rides. Our time at the BC was so cold the pool was a non-factor, but the one time we did get wet the sand at the bottom was nice, I will say.
BC Pros: Close to Epcot, but kids only really liked the Frozen and Soarin ride in Epcot. Us adults did very much enjoy being close to Epcot. We used an in-room sitter one night and strolled it without the kids.We could also duck over to France for cappucino and dessert, but you really need a park hopper ticket to enjoy this.
Close to Skyline, which was a nice way to take a leisurely journey to or from Hollywood Studios if you didn't mind transferring and waiting in two lines. Our kids loved the Skyline.
Boat to Hollywood Studios, (though we never took this)
Fitness center (Poly doesn't have)
Kids club (Capt. Hook's Pirate Crew) but we never used it because of one of the kids was 3 and you have to be 4. We used in-room sitters instead.
BC Neutral: Walk to Hollywood Studios. We adults didn't mind this but the kids complained how long the walk was. Our friends with kids also staying at the BC ended up Ubering to all parks aside from Epcot.
BC Cons: Big hotel with long indoor corridors. (Long carpeted indoor hotel corridors depress me, I'd rather have outdoor walkways when I am in Florida.)
We didn't get the balcony or patio we requested, unlike at Poly where we did get our request. (This could have just been luck, but thought I'd throw it in.)
Wait for bus to and from MK was long sometimes and sometimes very crowded. I much prefer monorail travel to bus travel. I felt so bad for the poor parents struggling to fold up a stroller. On the monorail, you can just roll the stroller on to the train.
BC food: BC lacks a robust quick serve and also doesn't have a casual sit-down, like Kona Cafe at the Poly or Ale & Compass at the Yacht Club.
BC coffee: The coffee at BC is so bad that one of the dads in our party would Uber to the Poly to drink their Hawaiian beans instead.
BC bars: The lounges at BC and Yacht Club felt a little grim. Poly has Trader Sam's and a lobby bar that has a view of castle and fireworks
BC lobby: I like walking in to an impressive high-ceiling lobby when I am paying this much money for a hotel and Beach Club's lobby is underwhelming.
Poly has a view of the castle you see every morning on your way to the lobby which feels magical.