There are studies that show, at least for large dogs, that hip and joint problems are less prevalent if the dog is not neutered before 1 year old (or not at all). Roughly, the intuition is that in males it allows the testosterone to have muscles grow to match their bones.
One citation: https://www.akcchf.org/news-events/news/health-implications-...
And another: https://www.dvm360.com/view/when-is-the-best-time-to-neuter-...
[1] https://www.banfield.com/en/about-banfield/newsroom/press-re...
For male cats neutering reduces territorial spraying (urinating in order to mark your space; the smell of the urine is also much stronger if ca isn't neutered).
If I remember correctly, it also reduces the risk of some type of cancer plus the risk of unwanted puppies.
The link between agression and neutering has been refuted by some studies.
However, I grew up with dogs in the 70's and 80's, and we never had them neutered, and they weren't going round humping everybody's leg. I think for now, I'll only consider it if I see specific behavioural or health issues that could be cured by it.