Only the corners of the LumenMax are diffuse material. The rest is specular like the LumenArcs.
In Sanjay's tests the LumenMax did have a lower peak intensity level over the test areas (ie. less intense hot spots, more uniform light field) which is apparently by design, and the reason for the diffuse/dimpled corners. Interestingly enough, however, if you compare the summary tables in the articles it actually delivered more total PAR to the 2'X2' and 3'X3' test areas than the Lumenarc.
As for which came first, IIRC the LumenMax was basically Sunlight Supply's answer to the LumenArc design. I think the LAs were around for quite a while in the horticultural market before they got popular with reefers.
At any rate, I doubt the minor differences on paper are significant in "real world" use. IMO either would be an excellent choice.