Here are some additional ways in which Daisy and Gatsby are similar, along with quotations:
Both Daisy and Gatsby are overcome with emotion after their reunion at Nick's house. Back at Gatsby's house, Nick says, "They had forgotten me [...]. I looked once more at them and they looked back at me, remotely, possessed by intense life." Both of them seem to be experiencing genuine, intense feelings for one another, as well as, perhaps, some disbelief that this moment has finally arrived.
Both Daisy and Gatsby enjoy irritating Tom, Daisy's husband. When Gatsby introduces Tom at the party he hosts and to which he invites Tom and Daisy, he calls Tom "'the polo player,'" to which Tom replies "Oh, no [...], not me." Gatsby continues to introduce Tom in this way, however, even though Tom would "rather not be [called] the polo player." Earlier in the text, Daisy accuses Tom of hurting her finger, and she calls him, a "great, big, hulking physical specimen." Tom, though, says that he hates the word "hulking [...] even in kidding." Daisy then repeats the word, and it seems like she just wants to get under his skin.
Both Daisy and Gatsby associate with cheaters. Daisy's best friend, it seems, is Jordan Baker, who Nick remembers being implicated in a golf cheating scandal some time before he met her. Someone "suggest[ed] that she had moved her ball from a bad lie in the semi-final round. The thing approached the proportions of a scandal——then died away." Likewise, Gatsby has some business with Meyer Wolfsheim, the man who fixed the World Series.
Here are some ways in which they differ:
When Daisy and Gatsby were separated by the war, Daisy lacked the patience that Gatsby had. Gatsby became worried because
there was a quality of nervous despair in Daisy's letters. She didn't see why he couldn't come. She was feeling the pressure of the world outside, and she wanted to see him and feel his presence beside her and be reassured that she was doing the right thing.
Eventually, Daisy married Tom, instead, because she couldn't wait for Gatsby.
Further, in the end, Nick describes Tom and Daisy as "careless people [...]——they smashed up things and creatures and then retreated back into their money or their vast carelessness [...]." Gatsby isn't careless at all. In fact, his persona is carefully crafted and managed, and he doesn't abuse other people the way Tom and Daisy do.