I wonder ... my initial response is the black would be hotter.  If we were painting a surface and putting a glass over it there is no doubt.  The light hits the black, and the infrared which passed through the glass as white light can't go back through the glass as easily, trapping heat.  But this is a surface in open air designed to shade what is underneath.

If the 85% mesh black absorbs the light and heat all that gets through to the surface being protected is the 15% open space. The heat is radiated away from the protected surface. If the white reflects it does that mean the light is reflected through the mesh as well as what passed on through to heat the protected surface?