Here's my 2 cents.
We own DVC at Poly so there's a bit of a bias here, I admit, but we've also stayed at BC three times - once in the hotel 20 years ago and then twice in a DVC studio. We absolutely loved our hotel stay and have the fondest memories of that stay. When we had a chance to stay at BC in a DVC studio, we jumped at it. The memories of the first stay and Epcot being our favorite park made it a no-brainer.
Then we arrived, and the experience was a definite letdown. At that time, the rooms were about to undergo a refurb (the only reason we go in was the planned refurb was pushed out a couple of months) and our room was in sad shape. But more importantly, we just didn't enjoy the resort - or the DVC portion at least. Easy access to Epcot was great, and the pool was cool, but honestly, that was the only draw for us. The good news was it was a split stay and we moved to the Poly after 3 days. Totally different vibe and immersion, and for us, so much more enjoyable.
A year later, we took our granddaughter (8yo) on a trip, and decided that we'd give BC another try (refurb was now complete) and figured she'd enjoy Stormalong Bay. Again, we were really disappointed. Access to Epcot and DHS was still great, but for us, BC Villas just doesn't feel particularly special. Granddaughter liked the pool, but she was almost too young for it and she was uncomfortable there unless one of us was really close by. She only went once and then didn't want to go back. We used the quite pool the rest of the time.
With your kids being younger, I think you'd find the pools at the Poly a better fit, and the proximity to MK if likely a better fit for you as well. You also have a quick 5 minute walk from the DVC buildings to the TTC where you can catch the Epcot monorail. Buses are normally shared only with the Grand Floridian and Poly is the first stop for both pickup and drop off. There are lots of great dining options at Poly, including a real quick service location, unlike BC where you only have a small location in the back of the gift shop with a very limited menu.
DW and I were just last week talking about how much we enjoy being at Poly and how, despite how much we'd like to like BC and enjoy the convenience of strolling into Epcot, we just don't really need to stay there again.
Hope this helps some.
Steve