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 Remember the Maine has cherry liqueur and absinthe. In parts, a Greenpoint is 4 whiskey, 1 vermouth and 1 Chartreuse; a Remember the Maine is 4 whiskey, 1½ vermouth and 1 cherry. By volume, the Greenpoint is 67% spirit, 17% liqueur and 16% fortified wine and bitter; the Remember the Maine is 61% spirit, 24% fortified wine and bitter and 15% liqueur. That makes them close cousins on the ratio map.
The Greenpoint is the stronger drink in the glass (25.9% ABV against 23.9%), but being smaller it holds about the same alcohol (2.06 and 2.00 standard drinks). Calories are close (about 229 and 227), but the Remember the Maine has more sugar (7.9 g against 6.8 g). Both are stirred and served in a coupe.