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."