Those are our 2 favorite resorts! They are the best of both worlds. We call one of them our "Epcot resort," and the other our "MK resort."
Stay at BC and walk to both Epcot and HS, enjoy the huge pool, boardwalk, Espn Club, rent surrey bikes and ride around the boardwalk, even walk to miniature golf.
Stay at Poly and enjoy the VIEW over the lagoon -- there's nothing like being in the sand or at the pool and seeing the Castle, boats, the GF....awesome. Watch Wishes right from the Poly too. Ohana is one of our favorite family dinner spots. Having the TTC right there gives you direct monorail to both Epcot and MK.
You can't go wrong with either one. BC does have the newly refurbished rooms right now...Poly has the larger rooms. BC has more of a luxury-beach feeling to it while Poly has more of a relaxed tropical vibe.
My vote is to split stay. Disney makes it easy to transfer, and you'll get to experience both of these awesome resorts.
If you choose to stay only at BC for your whole trip....
If you're not in a rush to get to MK, just start off your day in Epcot for a morning snack, etc., then just work your way to the front of the park and catch the monorail over to MK. It's definitely not a route to take if you're in a rush, but our family has always enjoyed doing this.