What do Caesar and Antony think of Cassius?

In act one, scene two, Caesar remarks that Cassius "has a lean and hungry look" and says also that "He thinks too much." The implication here is that Cassius is ambitious; he is "lean and hungry" like a wild animal looking for prey. Caesar is also suspicious of men, like Cassius, who think "too much," presumably because men who think "too much" are liable to plot and scheme, especially if they are "lean and hungry."
Antony, however, tries to reassure Caesar, saying that Cassius is "a noble Roman and well given," meaning that he is honorable, and has a good disposition.
Despite Antony's reassurances, Caesar is still wary of Cassius. He says that Cassius is too serious and that he doesn't love plays, listen to music, or smile as Antony does. Perhaps Caesar here is anxious that Cassius is unhappy, and unhappy men are, of course, more dangerous than happy men, especially when they are as clever as Cassius. Caesar also says that such men as Cassius "are very dangerous" as long as "they behold a greater than themselves." The implication here is that Cassius is, according to Caesar, someone who doesn't like to serve someone greater than himself.
In his speech later in the play, after Caesar has been murdered by Brutus, Cassius, and others, Antony repeatedly says to the gathered crowd that Brutus and Antony "are honorable men." He repeats this five times so that the phrase becomes laced with sarcasm. Antony thinks that the assassination of Caesar, and thus Cassius's part in it, was anything but honorable. At this point he likely regrets the reassurances he offered to Caesar earlier in the play.

When Caesar and Antony are talking in Act 1, Scene 2, they reveal themselves in the ways they judge Cassius. Caesar tells Antony:
Let me have men about me that are fat,
Sleek-headed men, and such as sleep o' nights:
Yond Cassius has a lean and hungry look;
He thinks too much; such men are dangerous.
Both men are looking at Cassius, who is standing nearby. Both have known Cassius for years, and yet both have entirely different impressions of him. Antony says,
Fear him not, Caesar; he's not dangerous;
He is a noble Roman and well given.
Caesar, however, speaks further about his opinion of Cassius:
Would he were fatter! But I fear him not,
Yet if my name were liable to fear,
I do not know the man I should avoid
So soon as that spare Cassius. He reads much,
He is a great observer, and he looks
Quite through the deeds of men. He loves no plays,
As thou dost, Antony; he hears no music;
Seldom he smiles, and smiles in such a sort
As if he mock'd himself, and scorn'd his spirit
That could be moved to smile at any thing.
Such men as he be never at heart's ease
Whiles they behold a greater than themselves,
And therefore are they very dangerous.
Caesar is right, of course. Cassius is very dangerous. It is ironic that while Caesar is judging Cassius, Cassius is also judging Caesar. Cassius is greedy and ambitious. He is a very serious man who spends much of his time thinking and planning, and he sees Caesar the same way. Antony must have remembered Caesar's words when his friend and mentor was killed and Cassius was obviously the mastermind behind the assassination plot.
What we can learn from Shakespeare—and perhaps even more from personal observation—is that people are all different and that we are foolish if we judge everyone by ourselves.