I would choose the Poly, if it were me. The Poly has larger rooms which all have a daybed that it comfortable to sleep upon. The BC has many rooms that only have two queens. With a family of five you would have priority on getting one of the BC rooms with a daybed, but it doesn't always work out that way. The BC will give you a rollaway, but that makes a somewhat small room even more cramped.
Also, if the MK is the park you will visit the most, then staying in a monorail resort is definitely the most convenient place to stay. Getting around in a huge place like WDW takes valuable time, so whatever adds to the convenience is a huge plus, IMO. Others have already mentioned this, but it is a very important point.
The grounds at the Poly are beautiful and part of what is really an incredible theme that has a very wide appeal. It is so relaxing. You feel pampered, but in a comfortable way that just feels right somehow. You feel at home and completely carefree. It is very special. The BC is also beautiful, but other than a walkway around the lake to the other resorts in the Epcot area, the grounds seem to be mostly enclosed as a part of the swimming complex. That is fine and we enjoy the activities at the BWI in the evenings when we stay at the BC, but the atmosphere is less 'earthy" and more cultivated. It makes a
difference when the grounds with lush foliage are all around you, like they are at the Poly. the torches lit at night are very romantic and watching Wishes and the Castle change colours across the lake is magical.
Storm Along Bay is great, but many people find it crowded and difficult to keep track of children there because there are so many twists and turns. Also, you have to leave the swimming area and cross the walkway to climb stairs to use the slide. The Poly pools are recently redone and are very nice - you can even watch Wishes from the main pool area.
If you like the look of Cape May Cafe, you can still dine there while staying at the Poly, but we feel that there are more and better dining options at the Poly itself than at the BC itself. If you go beyond the Poly or the BC to surrounding resorts you still have a better selection at the Poly, IMO - you have all the great restaurants at the GF (walk or monorail) and at CR(monorail). Now, to be fair, you do have World Showcase nearby for the BC, but only a few countries (UK, Canada, France) are really close by. The others are closer to the BC than any other resort, but they are still far enough away to not be 'convenience' dining, IMO.
Personally, I think staying at a monorail resort makes a huge difference. That is why we always stay in this area for at least part of every trip to WDW and continue to pay the insane prices to do so. YMMV, however.
Good luck choosing! Having stayed at both resorts many times in almost all categories of rooms, I feel confident in suggesting that whichever you choose, you will have a fantastic time! Enjoy!
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