Although, someone says that 여쭙다 is more honorific than 여쭈다,
officially there is no differences in the meaning.
You can use anyone in any case.
The difference is in the conjugation.
여쭈다 is conjugated as 여쭈어(여쭤) - 여쭈니 - 여쭈는
여쭙다 is conjugated as 여쭈워 - 여쭈우니 - 여쭙는