I own the Blichmann and I think it's a great burner. A little more costly than other burners, but it's extremely well made and worth the extra coin in my opinion.
I believe the regulators are different, but I'm not 100% sure. The Blichmann regulator has a precise control valve which I don't think comes stock with the Bayou. There's also an air damper to control the flow of oxygen. I feel like these two features increase the burner's efficiency. Relating to the frame, the frame is stainless steel, has adjustable retaining bars to keep your boil kettle a little more stable and optional leg extensions which are nice.