No expert here, but in general, I'd say the main advantage to a smaller diameter shaft/tip is reduction of endmass. Larger will result in a more rigid shaft with more endmass (LD tech shafts excluded).
But for the CM, it's not that simple. Factoring in variables like the wood's weight & density is really the key to figuring out the right diameter and taper for a shaft.
Some also say the shaft/tip diameter will affect the size of the contact patch made with whitey. To some extent that may be true, but I think the tip's radius or shape has more to do with that
...my 2 cents