The AF systems is identical in the 5DIII and 1Dx cameras. The 1Dx has a distinct advantage when tracking sports or wildlife, is colour tracking and face recognition. But it's a far more expensive and bulk camera and really is more suited to war zones, wild life or the riggors of track and field.
I fail to see the need for 12 fps at a wedding and the 5DIII's shutter is nearly silent with it's new silent mode. The 1Dx sounds like a machine gun in comparison. Many will buy a 1Dx because it's the new king of the hill, but the 5DIII is a more rounded and suited camera for weddings in my opinion. In fact, i can't think of one feature that the 1Dx has that the 5DIII isn't more suited for in the wedding role.
Just my take, your experiance and needs will vary!