The difference, by the numbers
Both have rye whiskey and sweet vermouth. Only the Greenpoint has Yellow Chartreuse, Angostura bitters and orange bitters; only the Red Hook has Maraschino liqueur. In parts, a Greenpoint is 4 whiskey, 1 vermouth and 1 Chartreuse; a Red Hook is 4 whiskey, 1 vermouth and ½ Maraschino. By volume, the Greenpoint is 67% spirit, 17% liqueur and 16% fortified wine and bitter; the Red Hook is 73% spirit, 18% fortified wine and bitter and 9% liqueur. That makes them close cousins on the ratio map.
The Greenpoint is the stronger drink in the glass (25.9% ABV against 25.2%) and holds more alcohol (2.06 standard drinks against 1.79). The Greenpoint has more calories (about 229 against 192) and more sugar (6.8 g against 4.1 g). Both are stirred and served in a coupe.