We consider the question of whether Gauss quadrature, which is very famous, is more powerful than the much simpler Clenshaw-Curtis quadrature, which is less well-known. Sevenline MATLAB codes are presented that implement both methods, and experiments show that the supposed factor-of-2 advantage of Gauss quadrature is rarely realized. Theorems are given to explain this effect. First, following Elliott and O'Hara and Smith in the 1960s, the phenomenon is explained as a consequence of aliasing of

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... oefficients in Chebyshev expansions. Then another explanation is offered based on the interpretation of a quadrature formula as a rational approximation of log((z +1)/(z −1)) in the complex plane. Gauss quadrature corresponds to Padé approximation at z = ∞. Clenshaw-Curtis quadrature corresponds to an approximation whose order of accuracy at z = ∞ is only half as high, but which is nevertheless equally accurate near [−1, 1].