Three words describe Edgar Linton: civilized, parented, and privileged. As the only son of a loving family, Edgar not only was the heir to Thrushcross Grange (and therefore had a secure future) he was loved and valued as a human being. While Heathcliff did get some affection during old Mr. Earnshaw's time, his status in the family was never of the only son and heir. He was an orphan brought in from the storm, and his parentage was never known. He was beloved of Cathy, but never had the emotional and social security that Edgar Linton had. In addition, Heathcliff had to invent himself, while Edgar knew his parentage and what was expected of him.
On top of this, Edgar was never abused; Heathcliff may well have been before he was brought to the Earnshaws, and Hindley certainly made Heathcliff's life a misery after his father died. This lack of suffering, this utterly secure bedrock of love and unassailed and legitimate place, is possibly the greatest thing that Edgar had that Heathcliff never had -- even when he was he master of Wuthering Heights.
Besides Edgar's enviable status and position in the world, he was bred down the hill in the relatively civilized atmosphere of Thrushcross Grange. Compared to Wuthering Heights, the Grange had social and educational advantages. There was less of a wild influence, both from the environment and from the manners of the people living there. Edgar is a smooth, indoor creature, compared to Heathcliff's wild and windswept outdoor persona.
All of Heathcliff's money had to be made by himself -- and we are led to believe that Heathcliff had to obtain it through less than honest means. Heathcliff left Wuthering Heights with nothing, and no one. Edgar never left, and never had to earn any money except managing his own inheritance. The person who struggles and wins, and the person who has things handed to them, often have very different outlooks on life. This was the case for Edgar and Heathcliff -- while obtaining wealth soured Heathcliff even more, the effect of secure and inherited wealth made Edgar pleasant, but perhaps a bit willful and complacent. He believes that Cathy is -- and always should have been -- his by right; he is unwilling to fight for her, while Heathcliff thinks the only way he can be happy is by dominating everyone. Neither is a perfect character, and they were both damaged by the things which happened to them, but in very different ways.
An antithesis would be described as a person who is the contrast and or opposite of another person. Edgar is an antithesis to Heathcliff as well as Heathcliff is Edgars antithesis. Edgar is the opposite of Heathcliff because unlike Heathcliff he was born into a family with status, and wealth. Also Catherine is able to walk all over Edgars pride without as much as a peep out of him whereas Heathcliff has no qualms about letting Catherine know how much she has hurt him. Also in they way they are both written Edgar is written someone type of golden boy while Heathcliff is masked as this dark brooding man.