That's just not the definition of efficiency that I use.
Efficiency is a ratio of how much _useful_ work something does over how much energy it consumes. If you change the numerator _and the denominator_ in the same proportions the efficiency doesn't change. Therefore, we cannot use "how much work changes" as a short-hand to speak to a chance in efficiency, _unless_ we also note how the denominator is or isn't changing.
So, back to my analogy, the efficiency is the MPG and the "work" is the number of miles driven. Those are different things. You can reduce the number of miles you drive _without_ changing the MPG.
> We are saying the same thing.
From my definitions of words we are absolutely, categorically, not saying the same thing.