We would choose BC over the Contemporary any day, but a lot of that comes down to personal preference. The Contemporary feels quite corporate compared to BC which is whimsically themed, light and airy.
Thinking objectively, if you are planning on spending a lot of time at Magic Kingdom, the Contemporary has some appeal. Similarly though, at BC you are walking distance to Epcot and a boat away from Hollywood Studios. Stormalong Bay is fantastic fun for kids and we love the set up there with Beaches and Cream right next to the pool and a convenient stop for ice cream, and Hurricane Hanna’s on the other side for food and refillable mugs station. Everything is very close, and Yacht, Boardwalk Inn, and the parks, are just a short distance away.
If I were personally looking at a MK area resort, I’d probably gravitate towards the Polynesian or GF as I prefer their theming and think it’s a much more immersive experience. We do love Chef Mickey’s at the Contemporary - it’s quintessential Disney - and the hotel amenities are great. I do think a lot of it comes down to what type of hotel and vibe you are looking for.