A cascade is basically a differential amplifier with one input grounded and the side with the real input has no load. It can also be seen as a common collector (emitter follower) followed by a common base. Since the input side has no load there is no gain on that side and the Miller effect does not come into play. In addition, Vds or Vce stays fairly constant which reduces distortion. Its advantage over the cascade is that it does not require as much voltage headroom. Its disadvantage is since it has two legs it requires twice as much current as a cascade for similar performance.
The complication in calculating the gain of cascaded stages is the non-ideal coupling between stages due to loading. Two cascaded common emitter stages are shown below. Because the input resistance of the second stage forms a voltage divider with the output resistance of the first stage, the total gain is not the product of the individual (separated) stages.