Certainly the quality of the source signal has a large impact on the resulting quality. However, analog signals that are poor quality to begin with from the cable company or deteriorated further by a low quality cable that is susceptible to RF/EMI interference will be FAR worse than a digital signal.
RF, composite, and s-video (and component too) usually carry analog signals, but there is no reason you couldn't use the same cables to send digital signals. I have digital cable and it comes to my box over the standard RF cable from the wall. You could use a composite video cable to send digital audio to your receiver. You could take that RF cable and solder on rca jacks and use it for digital audio too. The only real requirement is that the cables meet the specs for the transmission method; ie Video cables and digital audio cables need to be 75 Ohm.
This gets confusing, but I'll elaborate. Would it shock you if I told you that digital signals are analog too? Everyone knows that digital means 1s and 0s, right? But how do you send a 1 or a 0 over a wire that carries electricity?
You modulate the signal using any one of a number of techniques: PCM, PWM, PAM, Bi-Phase mark, etc. The fundamental difference between analog and digital is that analog is a continuous waveform (it is ANALOGous to the real world) whereas digital is discrete ("countable"). Naturally since we use the binary number system for digital, there are only 2 discrete steps: 0 or 1. How a 0 or 1 is represented is governed by the aforementioned modulation schemes. PWM (pulse width modulation) is the easiest to understand. The 'width' of the pulse determines whether it is a 1 or a 0. Say a 50 us pulse is a zero and a 100 us pulse is a 1. The amplitude of the pulse won't be anywhere near the amplitude of the corresponding analog signal - in fact it is constant for pwm - the 0 or 1 is encoded in the width of the pulse.
So... for an analog signal that is 4.7Mhz (480i cable signals) the wire has to be able to carry that frequency exactly, which is why a poor quality cable could introduce noise or attenuate the signal and result in a lousy picture.
For digital signals, bandwidth is in terms of bits per second and has nothing to do with the actual frequency of the signal you want to reproduce, except that the original analog signal was sampled at a frequency twice the highest frequency you need to reproduce (Nyquist theorem). So a digital transmission of 480i signals would result in 4.7 million bits per second and the amplitude of the pulses are low in comparison to the analog signal where they are exactly the original waveform. Thus, even a low quality cable will handle digital audio and video respectably. And of course, now that you have the signal in a digital form it can be more easily manipulated to do things like scaling or applying noise reduction techniques or changing color to greyscale, etc. For audio, it can be normalized, compressed, or have reverb added. All things that are more difficult to do with an analog signal.