None of the rhinoplasty options seem to visually change anything, with the sole exception being the insanely expensive 'The Hasselhoff'. I know this is a joke about the character designs of South Park, and was featured in an episode if memory serves, but is there any benefit in game? A person who will only friend you if you've got The Hasselhoff or something?
There's an achievement for beating the game while rocking the The Hoff Nose Job, and unlike the other options, it also provides some pretty significant visual customization. At a minimum, it's worth trying it and reloading a save for a laugh.
Beyond that, characters around you will remark on your 'new' face as you wander around South Park. Particularly if you're a Jew.