Depending on the white paint the visible reflectance is anywhere from well under 50% to nearly 90%.
Aluminum is 90%.
I don't care what form of aluminum. Foil, sheet, micrometer coatings. It's all 90-95%.
Aluminum also reflects radiant heat(IR) at 95%. So some people will warn you about building 'ovens' with aluminum & HID.
It also has about 80% UV reflection.
Those are all averages.
As for your question. I'd think metallic paint is better than matte paint, which is highly diffuse.
Reflectivity is the LAW of incident angle = reflectance angle. Aluminum and shiny, smooth, metallic surfaces do this directly(mirror finish). Diffuse surfaces uniformly spread the light over ~180 degrees(Lambertian reflectance).
For instace, 40,000 lumens according to Lambertian reflectance distributes about 277 lumens/angle. While aluminum(specular reflectivity) would redistribute 36,000 lumens.