From research, mostly aesthetic. Some people have given the 27won and Perrin bars some good reviews because they are single pieces (instead of the bar with a hinge on each end). I could be mistaken but I think if you notice any difference, it could be minimal.
Look at the Type R engine bay - notice that the strut towers are integrated into the firewall? The firewall acts as the brace. There is no benefit to adding a bar to this chassis. The same is true for a car like the S2000 with the X-bone frame - in other words, Honda didn’t just leave the bar off to cut costs, it’s completely unnecessary.