I had two stallions, a Friesian, and a Friesian/Warmblood cross. Both were VERY kind horses - I do think the Baroque breed stallions tend to be “different” then some of the other breeds. I am an AA rider who kind of learned as I went with my first boy (the cross), and then got my purebred as a yearling. I do think I was lucky that both had excellent temperaments, not sure I would have been as successful with a Warmblood or Tbred stallion.
I also know several breeders with Warmblood stallions, as well as a few Morgan stallions, and a friend with PRE stallions, so I’ve been exposed to many (and ridden several of those stallions). There IS a difference - I don’t know if it is more testosterone, or just a long time difference in how they have been bred and handled over the generations.
In general, stallions do have an innate sense of fairness - mares do too, so I suspect that comes from a higher level of hormones in the system. They need consistency, a routine, they need to KNOW the rules at all times. If they are punished too harshly or unfairly (in their opinion), they are more likely to react strongly to it. And it all goes back to - they need to understand the rules and boundaries. As for laziness, my two boys had incredible work ethics, they had a very strong desire to please.
But I do know several of the trainers I talk to who work with some of the other stallions, and they do say it is common to find stallions can be balky or lazy. I have seen that in a couple of stallions (Warmbloods), and one of those was gelded later in life, and it did help his overall laziness and tendancy to go to war, but he is still a quirky, lazy gelding that requires a very specific routine. He IS much happier now, and is with the same trainer who worked with him when he was a stud (although there were a few changes in trainer and ownership before he came back to her as a gelding).
A great deal of it has to do with the individual horse, as already noted. But there is also something to the joke about “brain surgery” - gelding does affect how the horse thinks, reacts, works. And if gelded too late, those patterns are already ingrained in the horse, so it won’t be a “miraculous cure”.
I currently have a late gelded pony - he was 8ish when gelded. And he does have stallion personality - he is highly opinionated, and needs a strong leader. He needs a very specific routine. And, interestingly, he is lazy, although he is smart, and is learning to NOT be lazy. He is NOT a brave character, interestingly, although he has a lot of bluff to make you think he is.
Personally, I LIKE the personality - I feel like mares and stallions are more engaged when they work with you. But you have to be more engaged too…