Theoretically, if you feed comparable signal to comparable cables, both should do equally well. But in actual practice the following is observed...
Over short lengths, < 30ft, in a relatively electro-magnetic noise free environment there will be very little difference.
Over greater lengths, analog signal cables are prone to picking up noise and signal degradation from transmission losses. In this situation, HVMI or DVI will yield a better result.
As if that was not enough, it also depends on the display. Some work better with analog signals, others work better with digital.