While the characters Brutus and Cassius are friends, they often do not share perspections, a difference that effects considerable conflicts in William Shakespeare's Julius Caesar. 

Early in the play, Cassius persuades Brutus that Caesar is dangerous because he seeks power:

Why, man, he doth bestride the narrow world

Like a Colossus, and we petty men

Walk under his huge legs and peep about

To find ourselves dishonorable graves. (1.2.141-144)

He, then, convinces Brutus to take action instead of thinking that there is nothing he can do by telling Brutus that

Men at some time are masters of their fates:

The fault, dear Brutus, is not in our stars,

But in ourselves, that we are underlings. (1.2.145-146)

Of course, Cassius's differing point of view, although able to persuade Brutus into joining the assassination, has disastrous results.  For, Brutus does not take Cassius's advice to kill Marc Antony; instead he allows Antony to speak, and the civil strife that ensues after Marc Antony's differing perspective on Caesar persuades the Roman mob to riot, is far worse than the reign of Julius Caesar.

During this civil strife in which Marc Antony, Octavius Caesar, and M. Aemilius Lepidus form the triumvirate who combat against Brutus and Cassius, the "evil that men do" continues as Antony dispenses brutally with Lepidus as of no more worth than his horse. Before battle, Octavius and Antony go to the field to exchange insults with Brutus and Cassius in Act V. 

So, too, do Brutus and Cassius continue to disagree.  When he expresses reluctance to go into battle because he has seen signs--a superstitious reaction more like that of Brutus--such as two eagles that have fallen and

Gorging and feeding from our soldiers' hands,

Who to Philippi her consorted us.

This morning are they fled away and gone

And in their steads do raven, crows, and kites

....their shadows seem

A canopy most fatal....(5.1.88-94)

Brutus has argued previously that

There is a tide in the affairs of men

Which, taken at the flood, leads on to fortune; (4.3.244-245)

When Cassius wants to wait, Brutus desires to attack.

In the ensuing battle, the growing conflict between Antony and Octavius has been foreshadowed by their earlier exchange about Lepidus.  When Antony tells Octavius to fight on the right, Octavius refuses to be ordered and does not.  Antony's insults to Brutus and Cassius also have their effect. For, Cassius takes the opportunity, then, to tell Brutus that he was always right about Antony:

Now, Brutus, thank yourself!

This tongue had not offended so today

If Cassius might have ruled (5.1.93-94)

By not waiting for the enemy troops to advance as Cassius has suggested, the troops of Brutus are enervated and become defeated.  Because of their disagreements from beginning to end, Brutus and Cassius are defeated.  And, because of his selfish intentions and disagreements with his triumvir, Antony is isolated from Octavius.  Indeed, conflicting perspectives have led to tragedy.

What are a few conflicting perspectives in William Shakespeare's Julius Caesar?

The essential conflicting perspectives we see in William Shakespeare's Julius Caesar concern the politics of the late Roman Republic. Most historians, both in antiquity and now, agree that the Republic had become disfunctional by this period, subject to endless factional strife and incapable of competently administering the vast empire that Rome had acquired. The conflicting perspectives were over whether the Republic was capable of being reformed and should be saved or whether Rome needed a strong dictator or monarch, i.e. whether it was a failure of the specific republic or whether republican government was in general ineffective and only a single strong leader could rule effectively. Secondarily, among those in favour of the latter option, there was a question of whether Julius Caesar would be a good leader. Brutus speculates:

It must be by his death, and, for my part,
I know no personal cause to spurn at him,
But for the general. He would be crown'd:
How that might change his nature, there's the question.
Act 2, Scene 1, Lines 10-34

Thus Brutus favours the Republic because he thinks that absolute power would have a corrupting effect upon anyone who had sole rulership of Rome, even a good man such as Caesar.