Hi Chuck,
I use a 6 jaw chuck. A couple of advantages are:
Less distortion on thin wall parts.
You can remove one or two jaws to clear protrusions on the part and still grip well. Think steam chest or fittings on a cylinder. Although a 4 jaw will probably be the better choice in this case.
You can remove every other jaw and use it as a 3 jaw if desired, although I don't remember ever doing this.
In my opinion, 3 and 6 jaw chucks of the same quality will have equal accuracy, but the 6 jaw will cost a little bit more. If yu are getting a new high quality chuck, I would get one that has an Adjust-tru or equivalent feature so you can adjust the runout for the most common used size of stock that you use. On even the best of self centering chucks the runout will vary on the diameter of the stock. On the better ones, the runout will vary less.
Gail in NM