Doesn't really matter much. Climbing from the south side is a little easier since you start about 500' higher up - but if you're riding from WC you'd need to climb those 500' to get to the south side starting point. And climbing from the south you get a little break from climbing at Rock City - makes it more pleasant but lengthens the time and distance to the summit.
I'd say the main advantage of doing the south and then north loop is just so you get the variety and views from both roads, but it will take a little longer than just doing an out-and-back.