Snooty:treating people as if they are not as good or as important as you. Conceited:having too much pride in yourself and what you do.
To me it sounds like both of them mean that the person is superior than the other people around. So accordingly I'd say that snooty emphasizes the fact that he treats people badly whereas conceited just say the the person likes to show off about qualities that he doesn't have. Something like that?
In my youth Lord Snooty was the aristocratic friend of other wise proletarian children (the Bash street kids) in the childrens comic "The Beano". Biffo is obviously of this generation as Biffo the Bear is another character in the same comic.