Mendelssohn's (1809-1847) most familiar pieces may be the Scherzo and Wedding March from his incidental music for Shakespeare's 'Midsummer Night's Dream' and the music for the Christmas carol 'Hark the Herald Angels Sing'. However, no less significant of Mendelssohn's work include his symphonies, notably the Italian, Scottish and Reformation; Violin Concerto; the concert overture 'Hebrides/Fingal's Cave'; and the oratorios 'Elijah' and 'Paulus'.

Brahms' (1833-1897) most significant works from a prolific oeuvre include his four symphonies; Violin Concerto; Hungarian dances; 'German Requiem'; and numerous songs for voice with piano accompaniment, most notably the Lullaby, which Bing Crosby and Frank Sinatra both recorded.

Neither composer would spend much if any of their adult lives in their native city Hamburg.

Mendelssohn's father Abraham, a banker, left for Berlin (1811) with his family fearing French reprisal for breaking Napoleon's continental commerce bank. As an adult Mendelssohn's duty stations have been Berlin, Dusseldorf & Leipzig, where he was principal conductor of the Gewandhaus (garment house) Orchestra, founded in 1781 & still active today, and conducted the first 19th century performance of Johann Sebastian Bach's St. Matthew Passion, which languished in mothballs after Bach's death in 1750. He also made 10 sojourns to the British Isles.

Brahms left for Vienna in his early 20s & made it his adapted home city.

More Info: en.m.wikipedia.org