In Act I, Scene II we see similarities which draw them together, really at the prompting of Cassius, who is trying to draw Brutus into the conspiracy.
First and foremost, both are concerned about Caesar being given too much power. The word "King" was literally and figuratively a four-letter word during this time, and both fear that Caesar is about to receive this honor.
"I do fear the people choose Caesar for their King" (Brutus).
It is this quote that Cassius uses to help launch into his conspiracy.
Second, they both can see benefits for Rome with Caesar out of the picture. Brutus is more noble than Cassius, so his motivations are more pure. He does not wish to see a tyrant take power. Neither does Cassius, but Cassius is also personally jealous of Caesar, which is part of his own motivation.