The difference, by the numbers
They have no ingredient in common: the El Presidente has white rum, blanc vermouth, orange curaçao, grenadine and Angostura bitters, the Tuxedo Old Tom gin, dry vermouth, Maraschino liqueur, absinthe and orange bitters. In parts, an El Presidente is 1 rum and 1 blanc vermouth; a Tuxedo is 1 gin and 1 vermouth. By volume, the El Presidente is 46% spirit, 46% fortified wine and bitter, 5% liqueur and 3% syrup and sugar; the Tuxedo is 49% fortified wine and bitter, 47% spirit and 4% liqueur. Different bottles, similar balance: that makes them close cousins on the ratio map.
The Tuxedo is the stronger drink in the glass (20.7% ABV against 19.5%), but the El Presidente is the bigger drink, so it holds more alcohol (1.55 standard drinks against 1.12). The El Presidente has more calories (about 188 against 116) and more sugar (8.4 g against 1.5 g). Both are stirred and served in a martini glass.