I have also used both and really prefer the pulling type. I used standard breast collars like this for many years and was often frustrated because I rode several hard to fit horses. It seemed that I always had to pull them super tight to keep them from dropping below the point of the shoulder. Little paint there was one of them.
Then, several years ago, my brother introduced me to the pulling style and I really liked the look of them so I improvised one out of an old standard BC and was really impressed. I used that until I found a pulling collar that I really liked. This is the one that I use now.
It fits a much wider range of horses from my Dad's 1300 lb tank of a QH
To a customer's little narrow 800 lb Arab
With no neck straps, punching holes, or other ways to improvise a fit on a horse.
That alone would be worth it to me but what you have heard is correct, they are more streamlined and don't interfere with the shoulders as much as a standard BC. Of course, a normal rider would probably never notice it. One of the reasons why this style started out *and remains most popular* with ranch hands and cowboys is because when you are pulling a 1000 lb cow, you can really feel the difference in the way the horse moves when his shoulders are freed up.
The question about pinching the withers wasn't directed at me but I'll go ahead and throw in my 2 cents. If it is adjusted properly, then there should be even pressure on all 3 straps; both that attach to the swells/d-rings and the one that attaches to the cinch. That way, when there is actually pressure applied to the BC, it just keeps the saddle from sliding back or sideways, it doesn't actually change the position of the saddle. Besides, if you had it tight enough just standing that it was pulling your saddle down, that would be the least of your worries because it would choke your horse enough that he would pass out.
Those that are designed for heavy duty work like mine and Appyt's will naturally have wider swell straps but there are BC's just like this that are designed for lighter work like trails that have more narrow ones that would likely fit your saddle.