Who dominates -- the living Caesar or the dead one?

This is a very interesting question!  One would be tempted to say that the living Caesar, the larger-than-life figure we see at the start of the play, is more dominant.  But truthfully, we see little of that Caesar, and while we hear about his grand deeds secondhand, we do not see them directly.  Instead, we see the living Caesar assassinated at the start of Act 3, Scene 1, and we sense his humility and weakness when he utters his famous phrase, "Et tu, Brute?"

The ghost of Caesar, on the other hand, continues to appear throughout the remainder of the play and does, in fact, have an effect on the plot there forward.  It is Caesar's ghost that serves as a bad omen to Brutus and warns of bad things to come at Philippi.  It is the thought of Caesar's ghost that ultimately drives Brutus to kill himself in Act Five.  Thus, while the living would naturally seem to be more dominant than the dead, both versions of Caesar play an important role within the play.