Most average to expert level pool players are picky about their shaft size, especially the Diameter around. Most standard pool cue sticks are about 13mm from the tip down but then you can get a 12 millimeter and even and slim as 11.75mm which does not seem like a lot of size difference but if you have a regular cue that you shoot with and switch over it is definitely a huge handling difference.
The theory between the different sizes really are meant for the tips of the cue stick. A 13mm tip will obviously have a lot more surface and is more for starting players or the average player who does not use a lot of trick shots or over use of English, versus a 12mm tip some people believe that since its a smaller surface area on the stick that your draw stroke, or your top strokes allow more precision shooting.
I believe that the real difference between the 2 size shafts is the extra weight of the complete cue stick, so if you have a bigger pool cue shaft your stick will be a lot more front heavy like a corvette sports car versus a smaller tips shaft most of the weight will be in the back much like a Lamborghini. Either way this really depends on personal preference because the only other way to compensate for either one is to get a Custom pool cue stick where the complete stick is perfectly balanced from the middle out.