The difference, by the numbers
They have no ingredient in common: the Naked and Famous has mezcal, Yellow Chartreuse, Aperol and lime juice, the Twentieth Century gin, Lillet Blanc, crème de cacao and lemon juice. In parts, a Naked and Famous is 1 mezcal, 1 Chartreuse, 1 Aperol and 1 lime; a Twentieth Century is 2 gin, 1 Lillet, 1 cacao and 1 lemon. By volume, the Naked and Famous is 25% liqueur, 25% spirit, 25% citrus and 25% fortified wine and bitter; the Twentieth Century is 40% spirit, 20% liqueur, 20% citrus and 20% fortified wine and bitter. Different bottles, similar balance: that makes them close cousins on the ratio map.
They are about equally strong in the glass (14.7% and 14.6% ABV), but the Twentieth Century is the bigger drink, so it holds more alcohol (1.51 standard drinks against 1.22). The Twentieth Century has more calories (about 193 against 171), but the Naked and Famous has more sugar (11.9 g against 10.5 g). Both are shaken and served in a coupe.