Re: Speaking of Canada...
"Two systems with identical input and output" - really can't generate significantly different amounts of heat, if "heat" is part of the "output" you're looking at.
If you're talking about, say, light output, or computational power, then of course your statement becomes true. But irrelevant, because the more efficient system (assuming, of course, that the system as a whole isn't intended to produce heat as part of its primary functionality) is the one that produces less heat.
In equilibrium, energy out == energy in. That's basic thermodynamics. It doesn't matter if some components are producing more heat than others - if you're looking at your console (or whatever) as a black-box system, then heat is an excellent proxy measure for how much total power it's using.