That question was directed at Sasha
OR
That question was directed to Sasha
what is the difference?
That question was directed at Sasha
OR
That question was directed to Sasha
what is the difference?
As noted above, 'at' is the correct usage.
'to' is appropriate only when the question is going to be sent rather than asked aloud:
After the meeting, the questions were distributed. All the questions about health were directed to Sasha.
Both are valid.
As reported from the New Oxford American Dictionary,
He directed his criticism at media coverage of the Catholic Church.
I suggest that he direct his remarks to the council.
Both the sentences are valid. In those sentences, direct means direct a comment/question to or aim a criticism to.