He has a similar aura to Tom

I would suggest: He has an aura that is similar to Tom's.

The sentences need slight adjustments to sound natural: 1. "He has a similar aura to Tom." 2. "He has a similar aura to Tom's." 3. "He has a similar aura to Tom." 4. "He has a similar aura to Tom's." Using "aura" in the singular is more natural, as "aura" typically refers to the overall vibe or atmosphere a person gives off, rather than multiple "auras."

And just to show how complex and flexibnle English can be: His and Tom's auras are similar.