
Not all harnesses give the dog an advantage for pulling - the Walkezee is excellent for pullers (google it), as is the halti harness. Incidentally, you also stop the potential physical damage done by putting all that pressure on just the throat, as well as spinal problems from lopsided pulling where constant pressure nudges vertebrae out of line.
I recommend headcollars as well, but only if they actually work (is that makes sense) - if the dog still tries very hard to pull they can cause trouble as well, and if the dog lunges at something there's the potential for neck damage. I won't use a headcollar alone on my Soli as she tries so very hard to pull on it that the potential for damage with her is high - I walk her on a halti harness and headcollar combo with a double ended lead, so she can't pull.