For my family right now, it's Poly over BC by a long shot.
We stayed in both in 2017 and for us, Poly was significantly better. Because (some random thoughts):
1. Awesome access to 2 parks (MK and EPCOT). My kids are young (5 and 3), so our most common park is MK. Monorail or boat to MK is awesome. You get great access to DHS and EPCOT with BC, but with your demographic (like mine, having a 3 year old), I bet you spend more time in MK than DHS + EPCOT combined.
2. The restaurant choices are miles apart. BC is a joke in terms of QS and Captain Cook's at Poly is AMAZING (if you like Polynesian food, but who doesn't?!).
3. We did our BC stay solely for stormalaong bay. Stormalong Bay is compelling, but not so compelling for a 3 year old. The Poly pools are just as good for a 3 year old. If you had a kid 6+, that would be a plus for BC.
4. The Poly resort is so well laid out. I like the longhouses and not relying on busy elevators (and long walks from the elevators). And Poly is so stroller friendly (due to the possibility of not needing an elevator at all to get to your room).
5. You mentioned you won't have a hopper, but one nice thing when we stayed at BC is that I walked to DHS on my own when my kids were napping (thanks to my wife for watching them). But we could do MK in morning (or another park) and I could go get my thrill ride on while the kids slept.
Note: My opinion will probably change when my kids are older. But then I'll choose BWI.