It seems that neither of these characters has a large amount of power at the outset of the play.
In the end, it is Antony who has achieved power and rallied the people of Rome behind him, though that is exactly what Cassius tried (and failed) to do.
If you're looking at the overall play, I would argue that Antony is the most powerful. It's interesting to see how the men's positions change throughout the play.
At the beginning, Antony is obedient to Caesar in the small role in which we see him (beginning of I.ii). Cassius, on the other hand, is manipulative and head-strong. He is trying to convince Brutus to join his enterprise and is defiant of the gods. However, after the assassination of Caesar, the power switches.
While mourning Caesar and eulogizing him, Antony is able to rile the commoners in to rioting and running Brutus and Cassius out of town, which Antony reveals was his plan the whole time. He become a powerful leader with Octavian, killing people who have crossed him in the past (IV.i) and leading the armies into battle with Octavian (V.i).
Cassius, on the other hand, becomes subservient to Brutus (IV.ii/iii). Cassius is still manipulative, but allows Brutus to make decisions about military maneuvers. Cassius is also pessimistic about the upcoming battle (V.i), and ends up having one of his men kill him while is face is covered, rather than honorably ending his life. Antony winds up victorious, but it is Octavian--Caesar's nephew and heir--who ends up on top and in charge.
Personally, I would say that Antony is more powerful overall in the play.
Between the two characters, many characteristics are shared, such as the manipulative side, being a good judge of character (despite some of Antony's misjudgements about both Cassius and Octavius), thus meaning that both characters are good politicians.
However, what sets Antony as more powerful than Cassius is how Cassius later on listens to Brutus' decisions. I would say that through his friendship with Brutus, and respecting,not arguing against, Brutus' idealistic decision making is one of Cassius' main reasons for downfall. Both characters are able to think on their feet quickly, but by listening and following Brutus' decisions, he is then led to his downfall.