If the US Treasury were to mint a $1T coin, how would that be different from printing the same amount of paper currency?

According to this article in Business Insider, there is a loophole in the law that theoretically allows the US Treasury Department to mint a $1 trillion platinum coin, deposit it at the Federal Reserve, and then continue paying its bills as normal. This would supposedly eliminate the need for Congressional brinksmanship with the debt level and avoid the periodic threats of government shutdown to serve the political needs of one party or the other.

Since the value of the $1T coin is determined by face value (as opposed to, say, the actual value of the metal in the coin) how would it be different from printing the same amount in normal currency for deposit in the Federal Reserve?