Chain is good for chafe prevention, especially aroung pilings when you are expecting a good blow. In an ideal world you would splice and eye around a thimble to connect to chain with a shackle. Good sound storm tie.
On the 150ton yacht I work on we keep mooring lines pretty tight. No motion unchecked or undamped by the lines stretching. My little 6 ton boat is always tied with slack for all the above mentioned motions to be accomodated. The big boat uses nylon braidline for most tie ups and the storm lines are nylon three strand with eyes and thimble to attach to the chains. The little boat uses all 5/8 nylon braidline, doubled when it blows and snubbers on the primary set.
To answer the OP, if that's still necessary, use the 3/4". If you have trouble fitting that around the cleats on your boat, consider replacing them.