As lynn30k identifies, once you are dead you have no say as to how your power is used or abused, therefore you need to be careful with your answer to this question. Whilst he was certainly powerful alive, his "power" is variously claimed or acquired by other characters to support their own needs. Arguably, depending on how you read the character of Marc Antony, you could say that he very cynically takes the power of Caesar and uses it to establish his own power for his own ambition. Caesar´s power definitely lives on, but you need to think through how it is manipulated and/or used by other characters.
Yes, I believe that he was more powerful dead--not just in the play but also in real life. There are some theories that Caesar actually knew about the assassination plot and allowed it to progress, not only because of his arrogance and a sense of immortality, but also because he had been publicly embarrassed on several occasions by his epileptic episodes. By dying such a public, violent death, Caesar demonstrates power even after death because characters (in the play) and historians alike still discuss or study why he was assassinated.
In the play, it is not simply that eventually Antony avenges Caesar's death; one must remember that everything that Caesar longed for comes to fruition. Eventually, his hier, Octavius, becomes the ultimate ruler of the empire--Caesar appointed him to do so, and so his wish is fulfilled. Likewise, Caesar's clever twist in his will to leave Roman citizens money and grounds influences many to view him in an even more positive light. Finally, Caesar truly desired to be king and had been declared "dictator for life" which is originally what drove Brutus to become involved in the conspiracy. I believe many would argue that Caesar's death eventually caused all emperors to be called "caesar," led to the title "czar" which denotes ultimate power, and paved the way for the decline of the Roman Republic and rise of the emperor.
I don't believe that a person's power ends upon his/her death. One doesn't have to be alive or know about his influence to be powerful, especially if we consider that inanimate objects (words) or symbols possess great power. Just look at North Korea--Kim Il Sun rules from the grave through his maniacal son Kim Jung Il. Their leader doesn't even have to utter words to control his people--they simply follow him because his deceased father was a godlike figure to them.
Caesar's power ended with his death. In the political vacuum that existed after the assassination, Antony grabbed power for himself by exercising his shrewd understanding of human nature. It was his ability to understand and manipulate others that accounted for his being allowed to speak at Caesar's funeral, turn the crowd, and plunge Rome into civil war. It wasn't Caesar-in-death who influenced the crowd. After all, moments before Antony's speech, Caesar had still been dead and the crowd had embraced Brutus.
It might be argued that Caesar exercised power after death because Antony sought to avenge his murder, but if so, it was short-lived. Antony's private speech over Caesar's body, mourning him and vowing revenge, seemed heartfelt, but as soon as Antony seized power and made his alliance with Octavius and Lepidus, his mourning and high-minded motives came to a screeching halt as he consolidated power and the spoils of war for himself. He purges the Roman Senate of those he perceives as enemies, he alters Caesar's will, and he cuts Lepidus out of the financial equation. It isn't Caesar or any reverence for his memory at work here.
The appearance of Caesar's ghost is a nice touch, but it isn't Caesar or his apparition that loses the war for Brutus and Cassius. The war is lost because Brutus is a terrible military strategist, Cassius is too weak to argue with him, and Pindarus didn't have a pair of binoculars on the battlefield.
Caesar's power ended on the Ides of March with his death. After that, the scramble for power became a jump shot, and Antony grabbed the ball and kept it.
Dead. People act on what they THINK was going on rather than finding out the truth. Also, Brutus is effected immensely by the appearance of Caesar's ghost on two different occasions.
Good question, good answer in post 2! Also, just in general, the power one has changes with death. The person is no longer around to say what they REALLY meant by their actions and words while alive, and both those things can be used and abused by others. Sometimes a person's power ends with their death, but in other cases there is a heightened interest in what the person's life meant. Their name can be used by others to their own ends.
In his funeral oration, Marc Antony tells the Romans
the evil that men do lives after them,/The good is oft interred with their bones;/So let it be with Caesar. (III,ii,76-77)
However, such is not the case with the conscience of Brutus. For, the good of Caesar exerts a tremendous power upon the soul and psyche of Brutus. Ridden with rue over having been "seduced" into the assassination of Caesar by his friend Cassius, Brutus engages in quarrels with Cassius throughout the remainder of the play. His inconsistency of behavior seems attributable to a guilty conscience--"the evil that men do"--as he sees Caesar's ghost shortly before his battle at Philipp, a ghost that ironically identifies itself as "thy evil spirit," promising to see Brutus soon. The battle at Phillipi is a disaster for Brutus. He commits both political suicide when he sends in his troops precipitately and physical suicide as he dies in the battlefield.
For Brutus, at least, Caesar's death is more powerful that his life: It has caused Brutus to be tortured by his "general honest thought" [Marc Antony's words in Act V] and to be destroyed by his guilt.
He is obviously more powerful dead than alive, since he also took down the conspirators and their armies. The conspirators were leading men of their times. His death also resulted in the purging deaths of others, and in innocent bystanders such as Cinna the Poet. At least there was stability when he was alive.