Some critics argue that Cassius, who is the driving force behind the conspiracy, is so agressive in his quest to rid Rome of Caesar because the two have such similar personalities--and that it is because of these similarities that Cassius is jealous of and threatened by Caesar's rule. Cassius seems to take pleasure in telling Brutus of Caesar's physical weaknesses (In 1.2, he describes having to pull Caesar from the Tiber River to save him from drowning and he also calls attention to Caesar's "falling sickness"), and uses Caesar's physical limitations to suggest that Caesar isn't worthy of the power and admiration he is receiving.
Also, in his soliloquy at the end of Act 1, Cassius says, "Caesar doth bear me hard, but he loves Brutus" (1.2.325), which clearly shows readers that Caesar does not like Cassius--or at least that Cassius perceives such a feeling.
Ultimately, Cassius criticizes Caesar for being too "ambitious" and justifies his plot to kill Caesar by claiming that he will be doing Rome a favor by ridding it of a dangerous leader. However, Shakespeare doesn't give readers very much insight into Caesar's character, so we aren't sure how much of what Cassius says is true. It is ironic, though, that someone as ambitious as Cassius (in terms of his organization of the conspiracy) has the same criticism for Caesar. In that regard, one could argue that the two have a similar character trait.