A mainspring delivers more torque when fully wound than when nearly run down. The fusee answers this mechanically: a tapered pulley connected to the barrel by chain or gut changes leverage as the spring unwinds, so the torque reaching the train stays nearly constant.
The cost is space and complexity. A fusee needs a large conical pulley, a chain, stopwork to prevent overwinding, and maintaining power if the watch is not to stop while being wound. All of this makes the movement thick and expensive to make and repair.
The going barrel drives the centre wheel directly from the barrel teeth. It is thin, cheap and robust, and it makes the flat watch possible. Its torque variation is then managed elsewhere: in hairspring geometry, in the overcoil, in careful isochronism adjustment, and by using only part of the spring's range.
English makers retained the fusee long after Continental practice had moved on, partly through genuine conviction about accuracy and partly because the English trade was organised around producing fusee movements. That conservatism is one strand in the decline of the English trade.
For a collector the practical point is dating and attribution. A fusee full-plate movement in an English silver case is a different research problem from a Swiss bar-movement going-barrel watch, even if both were sold in the same decade.
Neither system is simply better. A well-adjusted going-barrel watch with a good overcoil can outperform a mediocre fusee; a fine fusee chronometer remains among the most accurate portable mechanisms of its era.