The flatwound coil will yield higher powerhandling, and that is its primary purpose. If you aren't planning on insane amounts of power or SPL use, I'd get the copper coil.
That's because the link that's on the website isn't up.
The link to the forum is in my signature, BP power option is a back plate plug and some axial cooling vents machined in the motor, keeps the coil significantly cooler.