You would think... but if you don't have to run the 13 year old computer at full tilt, then the power difference may be minimal. The LEON SoS SPARC clones I used wound up consuming MUCH less power than modern intel cores.

And CPU power consumption is only part of the whole system. And a lot of the system power scales with bus speed rather than inverse CPU age. It's possible recent systems will consume more electrons than older systems.