In The Great Gatsby, what are the character traits of Gatsby and Tom that are similar?

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.