As with most engineering problems the answer does not lie in the underlying theory, but in the ability to best implement an approximation to the theory. These threads always get caught up in various misunderstandings of Nyquists sampling theory, quantization noise etc etc. I believe that the theories don't help us to explain whether redbook CD is better or worse than LP, since implementation of digital systems introduces errors (jitter being the main one) that are not accounted for by the simple theoretical models.
A sampled and quantized signal can IN THEORY exactly represent a bandlimited, limited dynamic range analog waveform, such that there would be absolutely no difference between the reconstructed analog waveform and the original waveform.
So, that said, I firmly believe that, in theory redbook CD can more accurately represent the sound of the master tape, since it has better linearity, dynamic range, signal to noise, channel separation etc etc etc than vinyl. Whether this is borne out in practise or not depends on many many real world variables, such as the quality of the ADCs and DACs, the mastering, the levels of jitter in recording, mastering, playback etc, anti-aliasing filter in the ADC, the implementation of a reconstruction filter.
However, those who write that digital can never be as good as analog because the digital signal looks like a little staircase (quantization noise is the technical term) are missing the point. Don't look to the theory ... look to the implementation.