Yes, to (grossly) summarize the conclusion of the paper: minres can outperform CG on the backwards error ||r_k|| / ||x_k|| whereas CG can outperform minres on t

Yes, to (grossly) summarize the conclusion of the paper: minres can outperform CG on the backwards error ||r_k|| / ||x_k|| whereas CG can outperform minres on the absolute error ||x^* - x_k|| and the energy norm ||x^* - x_k||_A.