The difference, by the numbers
They have no ingredient in common: the Death Flip has tequila, Jägermeister, Yellow Chartreuse, simple syrup and whole egg, the Mudslide coffee liqueur, vodka and Irish cream. In parts, a Death Flip is 2 tequila, 1 Jägermeister and 1 Chartreuse; a Mudslide is 1 coffee liqueur, 1 vodka and 1 Irish cream. By volume, the Death Flip is 49% spirit and 49% liqueur; the Mudslide is 67% liqueur and 33% spirit. Different bottles, similar balance: that makes them close cousins on the ratio map.
The Mudslide is the stronger drink in the glass (15.5% ABV against 13.4%), but being smaller it holds about the same alcohol (1.34 and 1.30 standard drinks). The Mudslide has more calories (about 257 against 231) and more sugar (19.7 g against 7.4 g). Both are shaken; the Death Flip is served in a coupe, the Mudslide in a rocks glass.