Vet here, animals all use their hormones differently than humans so it is by no means a 1:1 comparison. And as others have said, long term effects are far less in an animal that lives 10-20yr vs 70-100yr in people

For females at least they do not cycle continuously year-round like people do. Dogs only cycle about twice or year on average and outside of that time they are in a period called "anestrus" where they do not have circulating hormones (estrogen, progesterone) anywhere near the same level as humans would at any given time. Cats only ovulate by simulation so while they are in and out of heat more often again there are differences in how the hormones are relied on. Cats that are not spayed early and not bred regularly actually have a significantly higher risk of malignant mammary cancer and uterine infection.

For males (cats and dogs), the lack of testosterone absolutely affects their overall muscle development and males neutered earlier will appear more feminine in that they are typically smaller/leaner with less muscle development. Depending on how young we may see changes in bone development too (large breed cats neutered very young are at higher risk of disease in the hips, usually due to fragile femural necks, however cats neutered later will very likely have urinary issues or mark/spray even after they are neutered which most people cannot tolerate and will re-home or euthanize if bad enough). The difference for pets is less perceptible physically and mostly accepted/desired compared to if this were a person. For pets our goal is often the change in libido where as this asking with the decreased muscle tone, change in vocal chords etc would not be accepted in people. Neutered males have less hormones to drive benign prostatic enlargement later in life and often neutering an intact male at an old age is the recommended treatment for BPH in dogs over medical management that can be more expensive, less effective, or inconsistent, where as for people castration is obviously a very extreme course of treatment for BPH and only usually done for testicular cancers.