The difference, by the numbers
Both have Jamaican rum and passion fruit syrup. Only the Don’s Special Daiquiri has white rum, lime juice and honey syrup; only the Hurricane has lemon juice. In parts, a Don’s Special Daiquiri is 2 rum, 1 rum, 1 passion syrup, 1 lime and 1 honey; a Hurricane is 2 rum, 1 passion syrup and 1 lemon. By volume, the Don’s Special Daiquiri is 50% spirit, 33% syrup and sugar and 17% citrus; the Hurricane is 50% spirit, 25% syrup and sugar and 25% citrus. That makes them close cousins on the ratio map.
They are about equally strong in the glass (12.5% and 12.7% ABV), but the Hurricane is the bigger drink, so it holds more alcohol (2.71 standard drinks against 1.01). The Hurricane has more calories (about 423 against 172) and more sugar (37.6 g against 18.0 g). The Don’s Special Daiquiri is blended and served in a goblet; the Hurricane is shaken and served in a hurricane glass.