The idea that animals are better with pain is a very old school thought and it's becoming a best practice for vets to prescribe pain medication after surgeries.
Majority of animals hide pain and work themself to death to make owners happy, others are absolute babies and if they are sore they limp for days, which I'm glad my horse is an absolute baby so we can get stuff checked out instead of hiding shit
Owing to how livestock are commonly castrated young, no, not really lol. The only difference between the two is that most people only see one of those animals as pets.