I've also had both and have the Barred Rocks again.
It is difficult to compare breeds when you can't put them side-by-side at the same time. I wasn't especially delighted with either in the past - I thought. So, I'm committed to my Australorps.
But then, I've always like the Brahmas' personality - aloof, yeah, but I'd say independent, as well. The laying ability isn't the best or most consistent, I felt.
I wasn't too impressed with the Barred Rocks, as memory served me. And yet, they got off to laying quicker than my Australorps! One is just a real nice hen. The other is a bit noisy <shrug>.
I really enjoyed the beauty of my Ameraucana rooster. The little hen I had years ago, was a pretty good little hen. But personally and unless those Araucanas are really something special, I'd stay with the Brahmas and Barred Rocks.
Steve