In the consecutive speeches to the masses, Brutus and Antony appeal to different aspects of the angered citizens. Brutus appeals to reason and describes the idea of tyranny and the inevitability of a servile Rome under the heel of a King. Since the expulsion of Lucius Tarquinnius Superbus, Rome has been proud to define itself as a Republic. He momentarily has the sway of the crowd.
Antony appeals to the emotions of the crowd. Instead of describing an abstract idea, he produces Caesar's bloody corpse, and leads the crowd to a violent riot, fueled finally by a will promising them all 75 pieces of silver.
Emotion trumps logic, when masses are concerned. Watch the Willie Horton ad and test it yourself.