IF the chief justice is on the majority vote side, he can either write the opinion himself or decide who gets to write it. There was one long service chief who frequently switched sides when he was losing just so he could write the opinion himself.
The chief also sets the weekly agenda at meetings that decide which cases are to be heard. It doesn't sound like much but in practice it can really influence the direction of the court. He has considerable influence over which cases are heard, but technically each justice has equal vote in it.
The Chief justice presides over impeachments and swears in the president.
Thanks for the info. I have learned that it is more than ceremonial.