Children can be corrupted by power as easily as adults. Be certain the real problem doesn't lie with perceived favoritism on your part. Kids fight when one child feels slighted by the other. Often older siblings reach a stage when playing with the younger child becomes socially unacceptable. Especially do not force public play - this can lead to embarrassment and greater sibling resentment.
Kids fight out of habit.
Sometimes bullying and spitefulness become habits between siblings. Erase points for any meanness or belittling. Have a much desire prize for each child as soon a set number of points is reached. You will be amazed at the change in sibling interaction with such incentive and once the habit of unpleasant interaction is broken, new habits can more easily be formed. Sibling fighting probably will not lessen and cease without your involvement, but with consistency on your part - you can have a peaceful home.