In Julius Caesar, why did Antony have a change of heart about Caesar being the noblest man of all and then Brutus being the noblest man of all?

Antony did not have a change of heart. He never thought that Brutus was more noble than Julius Caesar. He thought that Brutus was the noblest man of all the conspirators. But he thought that Caesar was the noblest man who ever lived anywhere at any time in human history. There are two passages in the text that show clearly how Antony thought and felt about Caesar and about Brutus. One is to be found in the soliloquy he addresses to the dead body of Caesar in Act III, Scene 1. It begins with these lines:

O pardon me, thou bleeding piece of earth,
That I am meek and gentle with these butchers.
Thou are the ruins of the noblest man
That ever lived in the tide of times.

That is where he expresses his belief that Caesar was the noblest man that had ever lived. Then near the very end of the play, when Antony and Octavius are looking at the body of Brutus, who committed suicide on the battlefield, Antony says:

This was the noblest Roman of them all.
All the conspirators save only he
Did that they did in envy of great Caesar.
He only in a general honest thought
And common good to all made one of them.    V.5

Antony is saying that Brutus was the noblest Roman of all the Roman conspirators. In the first line he says "of them all," meaning only that Brutus was the noblest of the whole group of conspirators--but not that he was the noblest of all the Romans who had ever lived, and certainly not, like Caesar, the noblest man that ever lived anywhere in the world. Brutus, according to Antony's tribute, was the noblest man in a group of perhaps thirty Romans.

The fact that Antony does not hold a higher opinion of Brutus is also shown in what he says to Brutus and Cassius during their parley just before the battle at Philippi. Brutus tells Antony that he has stolen the Hybla bees' buzzing 

And very wisely threat before you sting.

Antony heatedly replies:

Villains, you did not so when your vile daggers
Hacked one another in the sides of Caesar.
You showed your teeth like apes, and fawned like hounds,
And bowed like bondmen, kissing Caesar's feet...      V.1

He is calling both Brutus and Cassius villains. He hates both of them for killing the friend he regarded as the noblest man who ever lived. He considers all of the conspirators villains, including Brutus, because of the way they went about killing Caesar. They had him outnumbered, surrounded, unarmed, unprepared. Brutus was the leader, and Antony must hold him responsible for what he considers butchery.

Antony can afford to be complimentary after he and Octavius have won the battle and Brutus is lying dead. But he obviously does not place him in the same category as the great Julius Caesar.