Birthdate differences calculation relative to earths orbit duration
The sidereal year is 6 hours and 9 minutes longer than a 365 day calendar year. To simplify your question, assuming you an your friend were born on the same date and time in 1983 and 1984 you would be 365 days, 6 hours, and 9 minutes older than your friend. 

Since there is no leap day between the two times you are considering, it doesn't affect the calculation.