I realize this won’t be exactly quantitative, but, not a lot. A normal punch to anything other than soft tissue can easily cause tearing to the knuckles. This can be your opponent’s face, or just a heavy canvas punching bag. This is part of why things like boxing handwraps exist.
Breaking bones, well, breaking your own bones is disturbingly easy as well. Unless my memory is off, there’s 27 bones in the human hand, and none of them are particularly well suited to suffering direct abuse. An improperly clenched fist can result in injuries ranging from dislocated joints to multiple breaks. Handwraps help to stabilize the fingers, and reduce the risk of breakage, while boxing gloves provide the hands with limited armor.
The entire point of boxing gloves is to protect the fighter’s hands, not to protect their opponent. The extra padding means they’re not going to be as prone to breaking bones in their own hands, or cutting their knuckles. The other side of this is, it makes it easier and safer to break your opponent’s skull with your fists. Something that normally wouldn’t be viable, because you’d turn your own hands into hamburger in the process.
There’s a real irony when it comes to professional boxing. When the gloves were first introduced, body shots were the norm, and the gloves were supposed to make the sport safer. What ended up happening was they made head shots safer, increasing their frequency, and in turn, made head injuries more common, reducing the overall safety of the sport. But, at least they made boxer’s fractures less common.
Tearing your knuckles is… basically aesthetic. Unless your character suffers from anemia, or if they’re dealing with a situation where they’re exposed to a potential infection, and they can’t have their hands treated, anyway. It’s unpleasant, but if it’s a choice between comfort and being horribly murdered, a little pain probably isn’t too high a price to pay.
You’re looking at using a disinfectant and bandaging the injuries. Literally, it’s safer than getting scratched by a cat.
Now, if they’re also being exposed to a blood borne pathogen in the process, that could be an issue, but that should be somewhat obvious.
Anyway, boxer’s fractures are unpleasant. This is where you have direct force against the knuckle, and it breaks the fourth or fifth metacarpal bone. The fourth metacarpal is the first bone you probably associate as your finger. The fifth metacarpal is the bone that runs to your knuckle through your hand.
In either case, you need to immobilize the broken bone, seek medical attention, and expect to need three to four months before you can use that hand again. Breaking the fifth metacarpal can easily end up requiring surgery to realign the bone. Ignoring this and trying to continue using the hand can easily result in more damage to the surrounding tissue.
If you’re wanting more information on that, then you’re in luck, because boxer’s fractures are a semi-common sport injury, so there is an absolute wealth of information out there on the subject.
Breaking your opponent’s bones is going to vary wildly based on what was broken.