Similar, but with a difference. Someone "pompous" is very self centered and believes himself to be very important. They really aren't thinking about other people specifically. A "snobbish" person believes he is better than others and acts that was explicitly, in speech and behavior.

"Snobbish" refers to social distance and social class. "And this is good old Boston, The home of the bean and the cod, Where the Lowells talk only to Cabots, And the Cabots talk only to God." "Pompous" is related to the word "pomp," dignified OR ostentatious display. It means someone who is being pretentious, someone who is putting on an act of phony dignity, trying to make themselves sound important. School principals, politicians, and administrators often use pompous language. A good example is George Orwell's: "Objective considerations of contemporary phenomena compel the conclusion that success or failure in competitive activities exhibits no tendency to be commensurate with innate capacity, but that a considerable element of the unpredictable must invariably be taken into account." That is a very pompous way to say "I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all."

for me, there are very similar/same. Pompous is the more formal word.