A 13 year old computer is gonna use a lot more power than a RPi, that's for sure.

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.