The difference, by the numbers
Both have white rum and Angostura bitters. Only the Art of Choke has lime juice, Demerara syrup, Green Chartreuse, Cynar and mint; only the El Presidente has blanc vermouth, orange curaçao and grenadine. In parts, an Art of Choke is ½ lime, ½ syrup, 1 Chartreuse, 4 rum and 4 Cynar; an El Presidente is 1 rum and 1 blanc vermouth. By volume, the Art of Choke is 40% spirit, 40% fortified wine and bitter, 10% liqueur, 5% syrup and sugar and 5% citrus; the El Presidente is 46% spirit, 46% fortified wine and bitter, 5% liqueur and 3% syrup and sugar. That makes them close cousins on the ratio map.
They are about equally strong in the glass (19.7% and 19.5% ABV), but the El Presidente is the bigger drink, so it holds more alcohol (1.55 standard drinks against 1.23). The El Presidente has more calories (about 188 against 156), with about the same sugar (8.7 g and 8.4 g). Both are stirred; the Art of Choke is served in a rocks glass, the El Presidente in a martini glass.