I recently met with a former professor of mine and we discovered something interesting about this scene:

On the one hand, an audience watching Julius Caesar would have been rooting for Brutus. From the first scene of the play, we are complicit in his conspiracy and we have been party to his interior thoughts like no other character in this play. Moreover, the actor that is playing him is probably at least the most famous actor in the company; in Shakespeare's time, he may have been the most famous actor in the country, if not the world.

On the other hand, Marc Antony not only delivers the better speech -- a speech that plays off of and negates Brutus' speech -- but also successfully sways the mob in the play to action; that mob is an obvious analogue to the larger mob that assembles at a playhouse to watch Julius Caesar.

One of the things that Shakespeare seems to develop over time is a knack for putting his audience through multiple contradictory systems of comprehension at the same time, which likely has the effect of deepening and enriching his plays. Compare this, by the way, to the second scene of Hamlet, where an audience, again following two contradictory schema, roots both for Claudius (the king and the voice of order) and for Hamlet (again a famous actor and the lone rebel at court against Claudius1)at the same time.
1. As this professor has written elsewhere, an audience is likely made somewhat uneasy, for instance, by Claudius' first speech in the play, which smoothly celebrates a repulsive fact ("our sister...have we...taken to wife"). However, after the relative anarchy of the play's first scene, an audience is in a weird position: both attracted to the order that Claudius represents and repulsed by the overly-orderly way in which he rhetorically joins the morally untoward.