Items are dropped even if both key pieces are already acquired.
If one key piece was acquired before picking up Filigree Feather, the next time the angel that normally drops the key piece Isaac currently has is defeated, it will drop the other key piece even with Filigree Feather equipped. (E.g. defeating Uriel while holding Key Piece 1 and Filigree Feather will drop Key Piece 2, but defeating Gabriel with the same items will drop an angel item instead.)
Key Piece drops are prioritized.
For example, after fighting Angels for the first time they will drop Key Pieces. If both pieces are picked up, next time Angels will drop items upon defeat.
If only one Key Piece is picked up, an Angel defeated in the next room will drop another Key Piece, and the next Angel in the same room will drop an item. If a remaining Key Piece is not picked up again, an Angel fought in a third room will drop the missing Key Piece again.
If both Angels are fought at the same time, only the last one defeated will drop an item.
Only angels that would otherwise drop a Key Piece will drop an item. This means that those who spawn during the Mega Satan fight, Boss Rush or those rarely found in closets in the Cathedral do not drop items, but ones found in some Super Secret Rooms and those summoned from Sacrifice Rooms do.