Which of the two is "worth" more?

It's easy to calculate. A stack of 100x $100 bills is 6.14 inches long, 2.61 inches wide, and 0.43 inches tall.

That's a volume of 6.89 cubic inches (112.92 cubic centimeters… and we'll use the metric system from here on out because it really does make more sense!).

$88.55 per cubic centimeter

A stack of 100x $100 bills is worth $10,000. So the paper money's 'value density' is about $88.55 per cubic centimeter.

Gold, on the other hand, is much more value dense.

A 1-kilogram bar of gold is 11.55 cm long, 5.25 cm wide, and 0.92 cm tall, for a total volume of 55.79 cubic centimeters.