I've got the same question posted on a couple pit bull forums and it seems like it's just for a cleaner look around the muzzle, but some people are saying it throws off there balance (I have heard that about cats but don't know any facts that back it up)
cutting the whiskers of cat's doesn't affect their balance, per say, but it does affect the cat in several ways. cat's whiskers are approximately the same shape (height, width) of their bodies. So cats use their whiskers to judge if they can fit into tight spaces. Cat's Whiskers are extremely sensitive to slight changes in air currents which helps them navigate in low light.
That being said dogs don't rely on their whiskers to such a degree, but if the question is just comes down to aesthetics, my questions is simply why? I'd rather let my dogs be au natural.
I thought whiskers for dogs were for sensory purposes....that seems a little mean to cut off something that can help an animal feel or sense things...but then again I also feel sad for dogs that get ears or tails docked off even though I know it is an extremely common practice, especially in AKC rings. I also get sad when I see cats who have been de-clawed. But I guess that's just me. I personally wouldn't want my ears to be cut or my fingertips removed just because someone else thought I looked better that way.
Whiskers are also a means of communication for dogs. If you ever see dogs interact in manners that are conflicting like tail wagging but growling and barking you can turn to several other body cues such as back posture, tail height in wag, philoerection, commisures of the mouth lax or puckered, and whiskers laid back smooth or flared forward.
Of all the things humans look for in determining what dogs are saying to us we rarely notice the whiskers. Other dogs notice them though. So with a dog like a pit which already has lost many body language communication devices such as ears and tail from human mutilation I think it further handicaps dogs and their ability to communicate effectively with other dogs. The only reason they are clipped is aesthetics or to aid in healing wounds inflicted in fighting (which is why ears and tail are cropped).
Many conformation show dogs have clipped whiskers again for a cleaner look. My dogs are floppy eared Goldens and it is harder in classes sometimes for me and other dogs to read their intent and not knowing sometimes how to read other dog's ears can make my puppy a bit annoying to other dogs. She doesn't see the subtle leave me alone signs because she doesn't know the lingo.
There is some sensory/protective function in the whiskers. Clipping them seems to be another aesthetic we humans feel the need to do just as we did in developing the breeds then deciding we want the floppy Doberman ear to stand up so the look is fiercer. I don't clip my dogs whiskers unless there is a physical reason to do so. Now and then puppy's eyebrows curl into her eye so I do clip those. Some breeds are prone to lashes or hair growing into their eyes.