Both plays take place in an immigrant and working class enclaves in American cities, thus contrasting the old-world values of the immigrants and the American aspirations of social mobility. A View from the Bridge focuses more on its immigrant setting (an Italian American community), while A Streetcar Named Desire opposes Stanley (of Polish American descent) to two Southern women, Stella and Blanche DuBois. Interestingly for your comparison, in the different rewritings of the play, Williams considerably toned down the immigrant component as the first version was all about an Italian family to which an Irish brother-in-law was later added. None of these characters remain in the final play.
In addition to the setting, both plays deals with feelings of jealousy and challenges to the male authority posed by a newcomer. Blanche challenges Stanley's authority in Streetcar and Rodolpho in A View challenges Eddie Carbone's authority continuing to court his daughter without his consent. Both Stanley and Eddie betrays their own families and communities denouncing Blanche and Rodolpho to the authorities for their past crimes (sexual promiscuity and a relationship with a young student for Stella, illegal immigration for Rodolpho). However, the result of these betrayals is quite different in the two plays. In Streetcar, Stanley initially horrifies his neighbors and his wife as Blanche is locked away in a mental hospital. However, the ending of the play leaves little doubt that he has reasserted his own masculine authority. On the contrary, Eddie has committed a crime of honor, causing other illegal immigrants to be arrested and he is despised by the community. In addition, his betrayal does not affect Rodolpho as his prospective marriage to Eddie's daughter makes him an American citizen. In the last scene, Eddie is (involuntarily?) killed by Marco, one of the men who were arrested after his betrayal (momentarily out on bail).