The dynamic range of vinyl, when evaluated as the ratio of a peak sinusoidal amplitude to the peak noise density at that sine wave frequency, is somewhere around 80 dB. Under theoretically ideal conditions, this could perhaps improve to 120 dB. The dynamic range of CDs, when evaluated on a frequency-dependent basis and performed with proper dithering and oversampling, is somewhere around 150 dB. Under no legitimate circumstances will the dynamic range of vinyl ever exceed the dynamic range of CD, under any frequency, given the wide performance gap and the physical limitations of vinyl playback.

Myth: Vinyl is better than digital because the analog signal on the vinyl tracks the analog signal exactly, while digital is quantized into steps

The Nyquist-Shannon sampling theory states that continuous-time (analog) signals and their corresponding discrete-time (digital) signals are mathematically equivalent representations of any bandwidth-limited signal, provided the sample rate is higher than 2X the bandwidth. All relevant advantages and disadvantages result from implementation details rather than analog versus digital signal representation method. Perhaps the most common method of storing a digital signal is with pulse code modulation (PCM). PCM is used on CDs and DVD-A.

PCM is sometimes characterized as producing a jagged, "stair-step" waveform. This is only partially correct; analog-to-digital conversion (ADC) does indeed use a sample-and-hold circuit to measure an approximate, average amplitude across the duration of the sample, and digital-to-analog conversion (DAC) does the same kind of thing, generating a rectangular-ish waveform, but this output is always then subjected to additional filtering to smooth it out.
Effectively, the ADC output sample values are interpreted as a series of points intersected by the waveform; the DAC output is a smooth curve, not a stair-step at all. Additionally, modern ADC and DAC chips are engineered to reduce below the threshold of audibility, if not completely eliminate, any other sources of noise in this conversion process, resulting in an extremely high correlation between the input and output signals. (Perhaps a better explanation: xiph.org's "Digital Show & Tell" video)

A related myth is that components of the signal near the Nyquist frequency must be square waves on CD (or digital media), and that vinyl (or any analog media) preserves pure sine waves. The premise is false. A square wave, or any wave that's not a perfect sine wave, is the sum of multiple pure tones (sine waves), by definition. So if you have a pure 22.05 KHz signal on CD (i.e., sample values +n, -n, repeatedly), the DAC may first construct a square wave, but the reconstruction filter then filters out everything above the Nyquist frequency, leaving behind a sine wave. The principle is the same even in complex waveforms. The end result is that the uppermost frequency components on CD are no closer to being square waves than they are on vinyl.