Interesting question. I see many more similarities between Gatsby and Nick or even Gatsby and Myrtle than I see between Gatsby and Tom. But I'll try.
The most obvious is that each man is filthy rich. Tom has had money all his life and lives in the fashionable East Egg section of New York. He buys polo horses, can keep a mistress in a furnished apartment, drives expensive cars. Gatsby has a mansion in West Egg, has "beautiful shirts," a cream-colored luxury car, a house with a swimming pool, and expansive yards big enough for lavish parties.
Both are in love with Daisy. And to each Daisy is regarded more as an object than as a true woman. Tom sees Daisy as a possession that he owns that he will let no one steal. At the confrontation at the Plaza Hotel, Tom is ruthless in his defeat of Gatsby and puts an end to any notion that Daisy will leave Tom for Gatsby. Gatsby too sees Daisy as one with a "voice full of money." He falls in love with because of her youth and her wealth. He desires her because she represents a time in his youth that he would like to relive.
Both have ties to the past. As Nick notes, Tom's life has been anticlimatic after his college football days. Gatsby thinks he can relive the past.
Both use Nick as a confidant in an illicit love affair Tom proudly displays his mistress Myrtle to Nick while Gatsby uses Nick to set up a tryst with Daisy.
DISCONTENT: Both men do not consider the value of what they have right in front of them, they push for something that is outside of the scope of the rules to achieve their own gains. For example, Tom breaks the vows of marriage to pursue a relationship with a woman who may be for all we know far less attractive than his own wife. This results in a dissatisfying marriage built on a facade. Gatsby on the other hand, breaks the moral code of mankind and not only allows but encourages a murder without any remorse, just so he can hopefully maintain a relationship with his reclaimed girlfriend.
SUCCESS WITHOUT EFFORT: We can tell from Gatsby's "gonnections", the rumors of his past, and his calls from Detroit and Chicago that he is in some kind of dirty business. He hasn't gone about building a company with his own two hands and then thriving from it. No, he is likely a well-to-do boot-legger. Tom, on the other hand, may have never worked a day in his life for all we know. His wealth is inherited and all he has to do is live.
LIARS: Both men lie to get what they want. Gatsby lies constantly to Nick and to Daisy both by what he says and by what he leaves unsaid. Nick asked him a question about the Midwest and Gatsby's answer had to do with San Francisco. That's not the Midwest. Furthermore, Gatsby lied about his family and background. Tom's life is a lie to his wife. He doesn't tell her about his relationship with Myrtle, but Daisy knows.