Correction to preceding wu by ramblebabble: Mozart died in the year Rossini was born and so couldn't have seen The Barber of Seville, for more information on the origins of both these operas refer to Le Nozze De Figaro.
Apparently the premiere of "Il Barbiere di Siviglia" was a complete flop. An opera of the same name had already already formed a part of the Neopolitan repertoire. Rossini decided to rewrite the opera and incurred the wrath of Neopolitan fans of the original piece. It is even said that some of the performers helped ensure that the premiere was a disaster.
One anecdote tells how the guitar Figaro was supposed to play on in the opening scene lost a string. This lead to such an outburst of laughter from the audience that the rest of the opera was drowned out.
Luckily for the rest of us, latter performances of the opera outside Italy achieved great acclaim and hence is still a favourite opera of many enthusiasts.