Jay Gatsby is the protagonist in The Great Gatsby, by F. Scott Fitzgerald, and Tom Buchanan is his nemesis throughout the novel. Both men claim to love Daisy, which is the cause of their dissension.
Each man's appearance is an indication of his character. Physically, Tom is a much more imposing figure, full of violence and aggression:
[H]e was a sturdy straw-haired man of thirty with a rather hard mouth and a supercilious manner. Two shining arrogant eyes had established dominance over his face and gave him the appearance of always leaning aggressively forward. Not even the effeminate swank of his riding clothes could hide the enormous power of that body--he seemed to fill those glistening boots until he strained the top lacing, and you could see a great pack of muscle shifting when his shoulder moved under his thin coat. It was a body capable of enormous leverage--a cruel body.
Gatsby, on the other hand, has a more refined wardrobe and displays an entirely different body language than Tom. When Nick sees Gatsby from a distance for the first time, Gatsby "gave a sudden intimation that he was content to be alone--he stretched out his arms toward the dark water in a curious way, and, far as I was from him, I could have sworn he was trembling." In contrast to Tom, Gatsby's body reverberates with solitude and longing.
Their attitudes are also quite different. While Tom displays blatant racist views in his conversations, Gatsby is not concerned by such matters. Gatsby's conversations are not innocent, however, as he is constantly talking about business deals which we learn are not particularly above-board. Not surprisingly, Tom is aggressive and opinionated when he speaks in social settings, and Gatsby is rather awkward and inept in them.
When Nick comes to visit the Buchanans, Tom rather arrogantly says, "I've got a nice place here"--something a guest would traditionally say to the host. When Gatsby is preparing for Daisy to visit, he says to Nick, "My house looks well, doesn't it?" Though Gatsby is also proud of his home, his question is not the same as Tom's arrogant assertions.
Both men claim to love Daisy. The Buchanans married because they both came from rich families and it was the expected thing for them to do. Tom demonstrates his love for Daisy by having a series of affairs with other women, even on his honeymoon; he does not work very hard to keep these affairs private, which is why the Buchanans move so much. It is clear in chapter one that Daisy--and everyone else--is quite aware that he is currently having an affair, though she does not know it is with Myrtle. Daisy has a bruise on her finger from Tom, and he clearly assumes she will just take whatever treatment he gives her because she always has.
Gatsby desperately loves Daisy and wanted to marry her, but he did not have a family name or money which were acceptable to Daisy's family. He does not see her for five years, and in that time Gatsby works feverishly to acquire the things which he believes Daisy needs in order to be with him. He buys a house across the peninsula from her and throws lavish parties in the misplaced hope that Daisy will one day appear. He yearns for her and longs for her, but he has created a romanticized version of her which dilutes his original, pure love for Daisy.
Daisy loved Tom once, but she loves Gatsby more. Tom is more aggressive than the idealistic Gatsby, so he gets the girl.