No, they are both exactly the same. $1 gets you ten times 10 cents (per share, in the sale) but gets you 10 times fewer shares than the $1.
They are both 20% falls. The mc in both stocks drops 20%, as does the value in your holding.
The point is that you see far bigger swings in small caps than you do in mid caps and even bigger swings in small caps v large caps.
In other words, you are far more likely to see a 20% drop in a stock with (e.g.) a mc of less than $50m than you are with a stock with a mc of $500.
The reason is that there are far more shares in a mid cap (thus more buyers) and you will have far fewer shares to sell (more dollars required to buy one share).
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