Depends on crew interpretation of effect of bird strike, certainly have to handle well in a hurry but if both engines are giving signs of malfunctioning …
It is generally believed that the forward fuselage will limit bird strikes to engine(s) on one side, but some experienced aviation people have challenged that. Certainly if birds spread across ground fly up when the see a huge bird coming they’ll get hit by both wings, I presume both ways depending on their position at taking flight, and possibly smear windshields.
FDR should give good clues as to engines, CVR may reveal crew’s thinking.