
Rye whiskey is American whiskey from a mash of at least 51% rye, aged in new charred oak. Dry and peppery where bourbon is sweet and round.
A Sazerac and a Manhattan lean on rye’s peppery dryness. Everything else in the American cabinet is sweeter, so a swap softens the drink rather than changing it outright.
Sweet and round where rye is dry and peppery. In a Manhattan the drink comes out softer and takes less vermouth; in a Sazerac, which has no vermouth to adjust, it simply loses the pepper.
In Canada "rye" is just a colloquial name for Canadian whisky, and there may be almost no rye in the bottle. It is softer and sweeter: in a Sazerac or Manhattan the peppery dryness disappears and the drink lands closer to bourbon than to rye.

Final Ward
Rye whiskey, Herbal liqueur (e.g., Green Chartreuse), Maraschino liqueur

Manhattan
Rye whiskey

Maple Old Fashioned
Bourbon

Reverse Manhattan
Rosso vermouth, Rye whiskey

Rye Boulevardier
Rye whiskey

Sazerac
Rye whiskey, Bourbon, Brandy

Sazerac (New Orleans Style)
Rye whiskey

Smoked Old Fashioned Godfather
Amaretto liqueur, Bourbon, Rye whiskey, Blended Scotch whisky

Toasted Old Fashioned Godfather
Rye whiskey, Bourbon

Vieux Carré
Rye whiskey, Cognac, Rosso vermouth

Calvados Sazerac
Calvados

Coffee Old Fashioned
Rye whiskey

De La Louisiane
Rye whiskey

Trinidad Sour – IBA
Angostura aromatic bitters

Old Pal
Rye whiskey, Red bitter

Roosevelt Cocktail
Rye whiskey

Billionaire
Rye whiskey

Brooklyn
Rye whiskey

Brooklyn (perfect)
Rye whiskey

Algonquin
Rye whiskey

Autumn Leaves
Rye whiskey, Calvados, Carpano Antica Formula vermouth

Oriental Cocktail
Rye whiskey

Suzerac
Rye whiskey

Waldorf No. 1
Rye whiskey