Really, they go hand in hand, but the acoustical environment of the room needs to be correctly evaluated prior to the proper sound system design. Way too many depend on only absorption data such as I provided AND modeling software such as EASE or Ulysses. I queried Dennis Fleisher PhD, my mentor, about diffusion characteristics of clay brick, and basically, there isn't any published diffusion data. Additionally, he said even the absorption coefficient data he had given me was based on 1950's manufacturing practices and 1950's bricks. Has their density changed, porosity, etc. etc. so to avoid the GIGO (garbage in, garbage out), he and I both prescribe to the preference of actually getting in the space, test the space with an impulse source, record the impulse source and analyze the data.
Have you read this thread?
Diffusion - possible to have too much?
It gives you an idea of what I do to test the room and analyze the data.