like many have said i think its the life they lead that affects how good/bad they are......mine leads the exact same life he would as a gelding with lots of social contact and turnout all day every day.
It should be noted that most of the working horses (and donkeys) in the world are stallions. The UK is very unusual indeed for routinely castrating our animals.
As the rider of a mare I regard it as my responsibility to manage her when in season.
I was at a dressage competition once and there was a stallion there, my mare when in season was a complete tart so I found out where the stallion was parked so I made sure I didn't ride passed him and checked what time he was competing so I could be as considerate as possible, as otherwise my mare I'm sure would have made it very clear that she wanted to make babies and that was a me problem not a them problem.
At home we used a menege that was home to a stallion, didn't go if she was in season, not fair to the stallion. When not in season they would hack out together. No problem
I have only had involvement with four stallions in my time.
Three of the four were perfect, literally you would have no clue they were entire based on behaviour, no different to a gelding to ride and handle. They had all been socialised growing up and manners instilled. In fact, one that covered in hand only mounted the mare when given the command to do so. He wouldn't have dreamed of mounting, even though stood sniffing the mare, until his owner gave permission.
The fourth had spent the first four years of his life locked away in a stable with no equine interaction. So when his new owners got him it was no wonder he fit the stereotype. He has come on loads but the cruelty he endured in his early years will no doubt always affect his behaviour.
we have one that ran with the herd till two, has been on different yards yet he is still very distracted by other horses when ridden and i would not trust him around other horses, he goes out all day every day and is a perfect gent to handle and ride , he is a very bold and courageous horse and his attitude to his status is consistent with his nature.
i have had others who are different and known loads of stallions mainly ridden its not just a matter of socialization more personality