Which of the following sentences is correct and why?
I replied a day earlier than she did.
I replied a day earlier than her.
If both of them are correct, what is stylistic better?
The former is "correct" and in fact you would still use "she" even if you did not include the word "did" at the end. However, almost no native speakers use "she" in this case when speaking casually. Most everyone would say "I replied a day earlier than her."