Depends on how the "efficiency" is defined. Efficiency in the broadest sense is the amount of net result for a given input. If you define the "efficiency" to, say, something like net Joule heat of an object relative to plug power on the heater, then you can get different answers than from the ratio of heater output relative to plug power.
Obviously, this is all highly dependent on the POV of the person doing the calculation, and the desired output of the calculation. As a systems engineer, it's the net result that matters, i.e., it doesn't necessarily matter that you have 99.9999% efficiency in one part of the system if there's a 0.00001% efficency somewhere else, particularly if there's another system that has even a net 0.01% end-to-end efficiency.
Therefore, in the OP, while the two systems may have the same unit efficiencies, it will be cheaper to use one in practice than the other, because its output is more efficiently coupled to the target.
TTFN
FAQ731-376