Tom Buchanan and Jay Gatsby both display moral turpitude, but for different reasons. One should view their acts of immorality in the context of their backgrounds.
Firstly, Tom Buchanan grew up wealthy and spoiled. The result of this is that he perceives whatever he has as an extension of himself, even the people he associates with. This means that as far as he is concerned, they are mere possessions. This holds true with regard to his relationship with Daisy. She was his prize possession. He had won her over with his wealth and status and she therefore belonged to him.
In this sense, he expects her to be dutiful and loyal to him and anyone who challenges this arrangement will pay a very high price indeed. Tom's arrogance also spills over into his other relationships - the affairs that he has with a variety of women, most notably, Myrtle Wilson. Tom does not care that she is married or that he too, is wed to Daisy. He has no qualms in committing adultery. Myrtle is but a plaything. One could argue that he shows greater commitment to Daisy for he, for example, slaps Myrtle violently when she mockingly cries out Daisy's name. He also vehemently defends his relationship with Daisy and even displays a certain amount of gentility when he confronts Jay about his affair with her.
This, however, is only Tom's idea of self-preservation. His arrogance cannot allow him to accept that his wife could have the temerity to reject him. It is for this reason that he threatens to expose Jay and later virtually plots with Mr Wilson to have Jay killed, by suggesting that Jay had been the one who had killed Myrtle and that he was responsible for her death. This shows that he lacks the moral measure to accept or tell the truth. Once again, it is all about him and he will not let anything stand in his way to get rid of those who threaten his position.
Because Daisy is but a possession, Tom does not deem it necessary to display her the same loyalty that he expects of her, therefore his extramarital affairs. He indulges his pleasure but expects her to remain true to him. His immoral behaviour does not bother him one bit.
Jay Gatsby stems from an impoverished upbringing. When he falls in love with Daisy, he is completely overwhelmed. He is a true romantic and she becomes his holy grail. Their relationship is interrupted when he goes to war, but he remains true to her. She however, grows impatient and marries Tom Buchanan.
Jay never gives up on his dream to win Daisy back. In his quest to win her hand he strives to attain as much wealth as he can. This desire leads him down an immoral path. He makes associations with the criminal underworld - bootlegging and selling junk bonds, which makes him enormously wealthy in a very short time. The depth of his criminality is clearly illustrated by his relationship with Meyer Wolfsheim, a man who had infamously 'fixed' the World Series. It is clear that Jay's association means that he has to know how such people, on the fringes of society, operate by using threats, violence and even murder.
Jay, however, chooses to be blind to this since he is obsessively driven by his desire to be with Daisy. Even though he has accumulated so much wealth, Jay remains loyal to Daisy, for he could have had any woman he wanted - the young ladies of the age would have freely thrown themselves at him. At his parties he remains aloof, driven by his great ambition. His parties were there only so that he could pique Daisy's interest and draw her closer.
Jay and Tom are complete contrasts in their attitudes to Daisy. Whilst Tom sees her as only an attachment, Jay is overwhelmed by her - she is the one and only for him. He wants no other. He is absolutely infatuated. Jay is overwhelmed by the idea of being in love with, and being loved by, Daisy. For him there is no other and therefore, he would not do anything to jeopardise his chances to be with her, least of all to have an affair.
Tom is the complete opposite. He risks losing Daisy by having affairs. His arrogance makes him believe that Daisy would never leave him and, in the end, he is disappointingly right.