Dad’s short answer: A corded upright with a strong motorized brush head, especially on medium or deep pile. Carpet needs sustained power and real agitation, and that's the one job where a cord still beats a battery decisively.

Why carpet favors corded

Getting embedded grit out of carpet takes two things working together for the whole clean: a brush roll driving into the pile, and enough airflow to carry what it loosens. Both draw serious power.

A cordless machine rations that power. Full strength in boost for a stretch, then it starts managing the battery, and on a large carpeted area you run out before you're done. A corded upright doesn't have that problem and never will.

There's also weight, which sounds like a downside and isn't. An upright's weight presses the head into the pile. That's part of how it cleans.

What to check on the head

Whether brush height adjusts, or the machine adjusts it automatically. Too high and the brush doesn't reach the pile; too low on thick carpet and it bogs down and can scuff the fiber.

Whether the brush roll can be switched off, for delicate rugs and hard floors.

Whether the head has a headlight. Sounds like a gimmick until you use one — on carpet in a dim room it shows you dust you'd genuinely miss.

And if you've got true deep pile or shag, this is also the case where I'd steer you away from robot vacuums entirely. Different question, same physics.

Dad’s Take: For a carpeted house, a corded upright is still the machine that gets it properly clean. Cordless is for the days in between.