I can think of all sorts of scenarios that could lead to the choice of Cat 1 in to wind or Cat 3 with a tailwind, so the premise of the question seems reasonable. Not being a pilot I can only guess, but neither approach sounds to be allowed under normal circumstances (exceed autoland tailwind limits or descend below Cat 1 minima) so I would expect you to divert unless an emergency compelled you to land. Once you call the emergency then you call the shots and you decide which rule you want to break. In the event that you request a runway change it could take a while to set everything up to open the opposite direction runway.