The difference
Campari and sweet vermouth in equal parts in both. The Old Pal adds Canadian whisky and is stirred and served up; the Sbagliato adds sparkling wine instead of a spirit, so it is lighter and fizzier, with about two-thirds of the alcohol.
By the numbers
The Negroni Sbagliato uses sparkling wine where the Old Pal uses Canadian whisky; both have Campari and sweet vermouth. In parts, a Negroni Sbagliato is 1 Campari, 1 vermouth and 1 bubbles; an Old Pal is 1 whiskey, 1 vermouth and 1 Campari. By volume, the Negroni Sbagliato is 67% fortified wine and bitter and 33% mixer and juice; the Old Pal is 67% fortified wine and bitter and 33% spirit.
The Old Pal is the stronger drink in the glass (18.7% ABV against 14.9%) and holds more alcohol (1.35 standard drinks against 0.88). The Old Pal has more calories (about 179 against 135), with about the same sugar (12.1 g and 11.7 g). The Negroni Sbagliato is built and served in a goblet; the Old Pal is stirred and served in a coupe.