Sometimes, though, it's just an older dog reminding the younger dog that they ought to be a bit more respectful/mind their manners/behave themselves.
My parents have a GSD who is 6 months older than my (much smaller) Kokoni. He is intact, she (for obvious reasons just mentioned) was spayed as soon as she could be. She lived, for the first 2 years of her life with my older (he was 13 when he died, would be 16 this year if he hadn't) Springer. Both pups were raised with the Springer. Now, my Springer was the most placid of dogs going, apart from grumbling when he couldn't catch a decent nap every now and then. The GSD respected him absolutely to the point that if we were visiting my parents (ie, the GSD's) home, and my Springer lay in the doorway, the GSD wouldn't do what most other dogs would and walk over him. He would wait until either I realised my dog was in the way and moved him... or the by then elderly and deaf Springer woke up from a nap and shifted himself somewhere else. In comparison, the Kokoni who lived with him would literally grabhim by an ear and drag him to the door if the postman knocked, whilst barking, because he just didn't give a shit - he'd worked out that the postman was not a threat to his household/family many years before.
The GSD, despite being only 6 months older, will (and always has done) tell the Kokoni off. If she goes off down a path he knows they're not meant to go down, he'll fetch her back - and I'm sure to passers-by, it probably looks/sounds like he's attacking her because he has her by the scruff and is growling/whining, it's hard to describe, but he is yelling at her. Except, he's not. He's reminding her, as the older dog in the family, that he's in charge and she is to do as sghe's told (she has perfect recall, as does he, but he does like to throw his weight about a bit). Yet she will also remind him that I'm disabled and he's not to climb all over me every ten minutes, by standing on my knees so they're eye level and growling. They have never had an actual set to. It's just saying "these are the the boundaries, don't wander past them, else I'll remind you why it's not a great idea for you to do so!".
The neuterued dog will still have ghormones going haywire and may even still be in pain from the op. Thus making them a little more reactive to the intact males bounding around. All you can worry about, though, OP, is your dog - and socialisation as well as continuous good training is key. Along with an understanding of dog's communication and how your dog yelping may be a "I'm a pup still!" pleas rather than the older dog having nipped at him. If your pup is going to disrespect another dog's boundaries, however, he's going to have to learn to back down - and one day he may well end up reactive, because he hasn't understood the micro-signals that all dogs (and cats) use to communicate. I used to watch my Springer's eyebrows as to when he'd had enough of two pups rampaging around him, weirdly, so it might work for you to learn your pup's own body language/facial expressions before exposing him to other, older, potentially in pain still dogs.
But also understand that not every dog being walked off-lead is dog-friendly. Or they have owners who got them on a whim and didn't bother to put the work in to training them, so they became reactive/nasty to other dogs. And I say that as someone whose daughter bought the Kokoni on a whim, as an 8 week old puppy, from a website... and then dumped her in my lap and couldn';t be arsed to do anything constructuve towards training/paying attention to her. Pre-lockdown by almost 3 years. We were her 3rd home in 4 days, apparently. I put the work in, and she is my little shadow as a direct result (and currently has a kitten climbing on her back, so clearly not as nasty as her grumble would imply).
Good luck