People will argue the merits of both, but "I" think the larger tip gives you more room to recover from a minor stroking error.
I play close to "center ball" (TOI) on almost every shot, if I am doing everything correctly for my style of play. I use English, as needed, but prefer to stay more on center and use the angles of the table to position the cue ball.
Other people prefer different angles and spin the cue ball more.
If you are playing center ball style, the tip diameter doesn't make any difference because you are hitting the center of the tip to the center of the cue ball, but if your stroke is a hair off and you are using a larger tip you have more tip to contact closer to the center of the ball than off to the side. The fatter shaft and wider tip also give "me" a better "sweet spot" feel for the cue ball. It feels more solid, like you are hitting the center of a tennis racket or when you hit a baseball really solid on with the bat.
If you are intentionally putting spin on the ball, you are using the edges of the tip and it really doesn't make a difference in tip size unless you are hitting the very, very, bottom of the cue ball. You will have a .mm less ability to hit the very bottom of the cue ball with a fatter shaft. Should this alarm you, I can draw the cue ball a table length or two with the fat shaft.
Watch the Taiwanese or Chinese players. Most of them play close to center as their style of play. Also, most of them use standard shafts (not LD) and, unless something has changed recently, they prefer 13mm shafts. The Predator 314-2 FAT shaft was created for the Taiwan market and it is 13.2mm.
It is what you get used to and feel most comfortable with. I started using a 14mm shaft back in the early 1970s and stuck with fatter shafts. I can put as much spin on the ball as anybody and I believe I have more control with it.
To each, their own. I'm sure there will be a lot of dissenting opinions. I've tried them all and I've stuck with what I like and play best with.
Aloha.
In edit: I'm not promoting or selling anything, but here is a reference where Predator backs up my statement about the Taiwanese players.
"The 314² Fat Shaft is the best option for players liking for that old-school, sturdy feel. Fat combines a thicker pro taper and a stiffer feel than the 314² with trusted Predator shaft technology to create the favored shaft of Taiwanese professionals."
http://www.billiardwarehouse.com/cues/predator/314-2_fat.htm
If you want to know why and when I changed to 14mm tips you can read the link below:
http://forums.azbilliards.com/showthread.php?t=240953&highlight=Herman+trout