I considered deleting the post, but this seems more cowardly than just admitting I was wrong. But TIL something!
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They can spend the same amount of money, but at any moment the one with 100s has more money. If you have 2 people each picking up 1 bill at the same rate at any singular moment the person picking up the 100s will have more money.
Since we're talking about a material object like dollar bills and not a concept like money we have to take into consideration it's utility and have to keep in mind the actual depositing and spending would be at any individual moment. The person with 100s would have a much easier/quicker time using the money therefore the 100s have more utility.
We're definitely not talking about this like a material object at the same time, though. There's no way for a single person to store and access an infinite pile of bills.
You can spend a 100 dollar bill faster than a 1 dollar bill, sure, but both stacks would have the same money in the bank.