Phase Offtset Bandlimited Saw Wave
Have you normalized the waveforms differently? The lowest point of the phase-shifted saw should be at amplitude -2 ln(2) / pi = -0.44 if the amplitude of the saw is normalized to -1 .. 1. The positive peak of the phase-shifted saw approaches infinity as you increase the bandwidth. So you could also have a clipping problem. Nonlinearities of the physical world affect the phase-shifted saw more strongly. The two waveforms have the same power spectrum and "complex envelope", but human hearing is more complex and may be able to detect some difference.