I stay away from analogies when it comes to electrical theory... the more I teach this stuff the more they seem to confuse a clear understanding of it.
Measuring current would indeed reveal an under-performing circuit, but measuring voltage (assuming you understand what's supposed to be going on) is almost always the better/faster route to diagnosis. If he was measuring more available voltage at the headlamp connector(s) when they were on (current flowing), then that indicates the upgrade harness has offered up less resistance in the circuit and the lamp assemblies are now closer to being the only resistors in the circuit. Circuit resistance (wherever it happens to come from) and applied voltage is what determines current flow. LEDs demand far less current than conventional lighting, meaning the shortcomings of the stock harness are just about negated; which, if I understand correctly, is why the OP didn't notice much of an improvement with the Putco harness upgrade.
Just re-read that conversation and realized DesertRat1991 is still running the stock headlamps... means his stock harness was healthy!