how much less hearing damage will a 9mm or .45 ACP cause than a .357 Magnum would?
Unfortunately, I have no data beyond that generalization.
Just from lots and lots and lots of range experience with a lot of different firearms, including multiple 9mm's .45's, and .357's. I can say that there are 2 main things which are going to give you a really dramatic drop-off in muzzle sound:
1) not having a barrel-cylinder gap (and no porting either! I have a .357 with both and it's abusively loud)
2) subsonic projectiles are "substantially" quieter.
.45 at subsonic speeds is really not all that loud. Probably the quietest of the 'effective' load options.
9mm at subsonic speeds is unbelievably quiet... unfortunately I'm not impressed with the effectiveness of subsonic 9mm. I recall being roadside with an officer who (at my request) was putting a wounded dear out of it's misery. I was curious about his terminal ballistics, and he was a rural cop who didn't care if i stood right there with him while he put the deer down. First round I had my ears covered, and I heard a pop that made me wonder if he had an under-charged round. Second shot I didn't cover my ears, it was still pretty quiet. 3rd shot, still very quiet, louder than a .22, but not by a lot. I surmised that he was using 9mm subsonic. I also surmised that it shouldn't take 3 shots point blank to kill an already mortally wounded fawn. If they made a highly effective 9mm subsonic (and maybe they do, i'm skittish about the idea though), then that would be your ideal round for avoiding hearing loss.
Worth pointing out, the pitch of the sound is as important as the total decibels. Towards that end, slower moving rounds tend towards lower pitched reports (particularly subsonic rounds which lack that high frequency 'crack').
And I'm sure the basics of reflected sound are a factor as well. For example: you'd be better off firing in an open room than in a narrow hallway.
If the bad guy shoots at you, then your hearing is probably screwed. Because the sound of a gun when you're forward of the muzzle is much much louder. Which is why reflected sounds indoors are such a problem in the first place. And why barrel-cylinder gaps or porting are so loud for the shooter.
One of the reasons I changed my HD gun is noise. I was using a ported 4" .357 8shot. After a mishap with a 9mm hydrashock and a faulty S&W safety de-cock lever... I had some permanent hearing damage (I was downrange of the gun that went off). Later, at the range, I noticed that my .357 was MUCH louder than anything else I was shooting, and most most of the other stalls too, and I began to worry if my HD gun choice would make me deaf if I needed to use it indoors. I started loading it with golden sabers which are a very mild load in .357 (only 430 ft-lbs). This was better, but still louder than any of my other guns. Eventually I decided I wanted to get away from having a barrel-cylinder gap and ported barrel. I picked up a glock 34, and once proficient with it, switched the 2 guns for HD role. I'm using supersonic ammo in the 9mm, it's not "quiet", but it's less loud than my ported .357 wheelgun firing cheap .38 reloads, yet has more punch than the .357 golden sabers.
But all this probably goes in the hearing thread. this is the 125gr/158gr thread
I still say 125's, because higher velocity means more explosive/reliable expansion, and if you're shooting at humans, 158's will over-penetrate quite a bit. that's just thinking about it logistically, above and beyond the 1-shot-stop stuff which seems to also favor 125's as well.
I'm not a fan of hydrostatic shock or anything, but you do want to transmit the bullet's energy onto the target (preferably in the form of a permanent wound cavity as wide, deep, and violent as possible). 125's will release most of their energy in a target, while still having enough left over to make an impressive exit wound (increased bleeding, etc). The higher velocity round has a better chance of making hollopoints perform correctly through clothing and such. Meanwhile the 158's will have more penetration, and likely carry a great deal of the round's energy beyond the target, meaning less of the energy is "used" effectively to create wound trauma.
Against humans .357 ranges from excellent penetration to overpenetration. use faster-lighter loads with less sectional density to keep it leaning towards "excellent penetration" and not overpenetration. Unless you plan on shooting people through obstacles, then use 158's. But shooting at someone who's hiding behind cover is not considered "home defense" in most states.