Hmm. Could it possibly be a firewall issue on your router? Routers will sometimes block certain ports but not others. Baconcow, if you know what you are doing with your router (and it's not locked down by your Internet provider), you could assign your Xbox One's IP address to the DMZ on your router which would bypass the firewall completely. Then you could try a BC game and see what happens.
I will try the DMZ thing. It is odd that I am able to play these fine on my Xbox 360 but not the Xbox One.