A chain rarely runs in a straight line, and presents 115 or do links, each with their own opportunity for inefficient. A shaft in its simplest firm has only 2 moving interfaces.
A well maintained modern chain set up us hard to beat for efficiency, but it doesn't take much for the lazy rider to sent that plummeting.
Noise is indeed a door of energy, but no where near as energy rich as heat. Feel a chain, especially a worn or dry one after a long ride and it'll be warm. Feel a gear housing on a shaft with helical cut gears and it can be too hot to touch.
And a shaft can be lighter than a chain - yup, you got the housings, but the shaft itself can present less mass to accelerate than a chain.
Chain any day, but don't dismiss the principle of the shaft, although but the time it's tidied up and made user friendly it's picked up a lot of inefficiency, although compared to a poorly maintained chain-drive hack its still more efficient. Like I say, if you're wealthy, don't do huge mileages and would sooner die than wield a spanner then it's liable to be a more efficient option than a half dead rusty chained euro racer.