Good question. There are some black metal roofs out there with reflective pigments in the coatings. They usually have a Total Solar Reflectivity in the 25 - 27 range. White, on the other hand, is around 65.
The reflectivity of a reflective pigmented black metal roof will be higher than a standard black asphalt shingle roof.
I do always mention when folks talk about black metal roofs -- a black metal roof is very black -- much more black than a black asphalt shingle roof. Sometimes it can surprise people once it's installed.
Yes, darker colors can be more susceptible to fade. Using a PVDF chemistry coating will provide your best fade resistance.
I would encourage you ... look at more than just roof reflectivity ... look at ventilation and thermal breaks and even additional radiant barriers as ways to gain energy efficiency. I have some additional information I can send you if you wish. Drop me an email at todd@asktoddmiller.com and I will reply with it.
We live in Florida, obviously a very hot climate and we are building a home with no existing trees around so we will have no shade. Will a black tin roof attract to much heat and make our home hard to cool?
Also, with direct sunlight and no shade will this fade?