My answer is not from Jyotish, however from Hindu mythology.
Story says, the hunter who did linga archana using the vilva leaf on Shivaratri night, was reborn a great king. Obviously the two personalities cannot be the same. Like this, many instances or narrations of former sinners born saints, kings, etc, out of good karma.
Therefore, the personality maynot be the same - for example, if you an Aquarian (like me) with strong Saturn influence on lagna, you might be philosophical and lonely. Whereas, if you are reborn into Leo lagna, with a different planet influencing your ascendant and moon, you definitely will have an altogether different personality.
But what might repeat, is an innate feeling of generosity (with good karma) or vices like obsession (in case of bad karma) until that karma gets expended.