I was experimenting with draw recently and noticed that I got the best draw with an 11mm shaft, dime shape, and soft tip. I also got more English than with a 13mm nickel medium tip.
It was sort of like the 13mm was a big truck with un-responsive slow steering whereas the 11mm was a precision sports car which could do all sorts of manuevers. I guess because the tip/shaft is smaller, it seems like there are more positions you can use for English when aiming at the cue ball. And for draw, it seems that with a smaller tip, you can aim lower. (May be my imagination?)
The down side to the 11mm shaft and soft tip was that long hard shots would sort of fizzle out. Could not get any power or speed out of a shot.
And the down side to the 13mm tip was that I could not get a dime radius (better draw) on it as the curve would go down to the ferrule.
So I settled on a 12.5mm shaft with a Moori III M dime shaped tip. Now I get better draw, but can also hit hard long shots with speed and power. (By better draw, I mean I can more predictably draw back the cue ball a specific distance; 1/4 diamond, 1/2 diamond, 1 diamond, 4 diamonds, etc.)
I got a lot of ribbing from some of the guys by switching from a 13 mm to a 12.5mm shaft. You can imagine the comments. I got back at them by pointing out that they were 1/2 mm off on each shot I saw them miss.

They were not laughing when I won 1st in a tournament the other night. One of the key shots I needed was a draw shot - only draw shot I needed that evening, but I got the cue ball back *exactly* where I needed it.
Note that some players shape their tips by "eyeballing it" with sandpaper. I've noticed the biggest difference in English is with different shaped tips. Try a quarter shape, then a nickel shape, then a dime shape. Therefore I think it is *very* important to keep an exact shape on my tip using a tool which will give it an exact shape. (Not "eyeballing" it with sand paper....)