A 6" barrel anything is "quieter" than a 2" barrel, because the muzzle is a little further away from your ears.
Its not a lot "quieter", but there is a noticable difference. The .357 Mag is LOUD. Combining supersonic speed and the small bore size, it has a bark unlike anything else.
Now, remember that the .357 Mag was not designed as a self defense round. And for many years was not even available is mid size or pocket size guns. The fact that is has proven to be a very effective selfdefense round is a bonus, but it was never intended as such originally.
It is a well documented fact that most people experience what is called "auditory exclusion" during a self defense shooting situation. What happens is your mind is so focused on the other gun, his gun, etc, that while your ears hear the shot, your mind doesn't notice it. This does NOT prevent hearing damage, it just means you don't notice it until later, when the main stressor is removed.
Fire a .357 under any other conditions in a enclosed space (room, automobile, etc) and you WILL notice the blast, most likely to a stunning degree.
If there is one thing movies and TV drama teach us, (besides poor/dangerous gun handling) is that you can shoot guns indoors without any hearing protection, and be able to hear normally afterwards. This is simply NOT TRUE. IT doesn't matte what you shoot, even a .22 will cause ringing in the ears, and larger rounds (even low pressure, low speed ones) will give you hearing problems, and high intensity rounds like the .357 can leave you temporarily deaf, ears ringing for day (or even longer) after your hearing returns. And your hearing will not return fully. There is damage, and it can be measured. Do it once, and you won't notice the damage, after your ears recover, but it will be there.
Do it several times, and you will soon reach the point where you will be able to tell that there has been damage. With our current medical technology, the damage is permanent.