You're right when it comes to the entropy of the universe versus the brain. But in terms of what intuitively feels more complex, I still think the brain. It feels like the universe is easily summed up in a few equations and the brain is much more than that, all in one ball. Plus I think there's a part of the brain that goes outside the physical world.
As long as the brain is inside the universe. My theory is that there's a part of everyone which is outside this world and sticks to them right outside in 4D space. Like a soul but minus the religious nonsense. This part could be under laws more complex than the universe.
Btw also the reason I have no intention of trying to prove this further, is because I've also had to deal and argue with someone else in the past in this fandom who wouldn't stop trying to prove that the brain was bigger and I really don't feel like trying to argue about that again. But as I can see you are respectful of my opinion, which (in itself) I also respect.