A poster on this thread has claimed:

the only major difference between [the two sexes] are cumulative changes as a function of time and certain life changes that are influenced by sex hormones.

On a biochemical level, yes, I would view them [the two sexes] as the same. If that weren't the case, there would be a need for a male-only covid vaccine and a female-only vaccine.

In response, I've selected a few passages from research on the topic:

The effects of gonadal hormones have been studied much more than sex chromosome effects, for several reasons. The theory of sexual differentiation emerging from research in the 20th century pointed almost exclusively to gonadal hormones as the proximate sex-biasing factors, so any program of research on sex differences focused first on hormones. This focus was usually rewarded, because most sex differences were found to be influenced by sex hormones. The resulting large literature on sex hormone effects gives the impression that hormones dominate as the causes of sex differences. That inference may be true, but has not been tested rigorously...

Especially since 1990, there has been increasing realization that sex differences occur throughout the body. Tissues not specialized for reproduction, including non-reproductive areas of the brain, function differently in females and males, and are differentially affected by disease in the two sexes (US National Institute of Medicine Committee on Understanding the Biology of Sex and Gender Disorders, 2001). In some cases, sex differences in disease can be dramatic...

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5369239/#R68

Some more passages snipped from the same paper that are relevant:

Before 1980, investigators in this field had predominantly studied the most obvious phenotypic sex differences, in the gonads, external and internal genitalia, and behavior (Arnold, 2002). These investigators viewed themselves largely as reproductive biologists and psychologists, because of the function of the tissues or behaviors they studied. Earlier in the 20th century, investigators had asked the fundamental question whether phenotypic sex differences were dictated by the sex chromosomes or by gonadal secretions. For the birds and mammals, the answer was that sexual development outside the gonads was controlled by gonadal hormones. Experiments showed that changing the gonadal hormones could profoundly change the sexual phenotype of reproductive tissues other than the gonads. For example, it was possible to give male hormones to genetic (XX) females to make the genitals or behavior similar to that of a male, or to take male hormones away from genetic (XY) males to make their genitals and behavior like that of females (Jost, 1947)...

Several developments have contributed to a revision of the old dogma. One is that the revolution in molecular genetics has given us a much better understanding of the genes on the sex chromosomes, their evolution, and function (Deng et al., 2014; Graves, 2006; Lahn and Page, 1997; Skaletsky et al., 2003). This new knowledge shows that the inherent inequality of X and Y genetic material in the two sexes has effects throughout the body, not just on the gonads. A second major influence has been that various experimental findings have uncovered cases in which the old theory was inadequate...

At the same time as these developments, the study of sex differences was expanding beyond tissues related to reproduction.

For example, dramatic differences have been found in the ways the kidneys, hearts, lungs and respiratory systems function in male and female humans and other animals.

In the past, scientists studied male physiology and applied findings to women, so studies such as the new USC research underscore the importance of biological differences.“Profound differences distinguish the male and female kidney,” McMahon said. “The kidney is the body’s regulator of fluid balance, and since women bear offspring, there are likely critical differences required in the mother for the benefit of both mother and offspring.”

The findings can benefit human health by improving an understanding of genetic programs that may influence drug trials, drug toxicity and cellular reprogramming, he said.

https://www.technologynetworks.com/cell-science/news/stem-cell-scientists-reveal-key-differences-in-male-and-female-kidneys-326828

Over a period of 10 years, the weight of the heart’s main pumping chamber — the left ventricle — increased by an average of 8 grams in men and decreased by 1.6 grams in women. The heart’s filling capacity — marked by the amount of blood the left ventricle can holds between heartbeats — declined in both sexes but more precipitously so in women, by about 13 milliliters, compared with just under 10 milliliters in men. The differences in size, volume and pumping ability occurred independently of other risk factors known to affect heart muscle size and performance, including body weight, blood pressure, cholesterol levels, exercise levels and smoking.

https://www.hopkinsmedicine.org/news/media/releases/male_and_female_hearts_dont_grow_old_the_same_way

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5980468/

Regarding the view that "if there were significant differences between the sexes, then we'd need a COVID vaccine for each sex," an important journal article from 2014 about vaccines in general, and flu vaccines specifically, is relevant:

Biological (ie, sex) differences as well as cultural (ie, gender) norms influence the acceptance and efficacy of vaccines for males and females. These differences are often overlooked in the design and implementation of vaccination strategies. Using seasonal and pandemic influenza vaccines, we document profound differences between the sexes in the acceptance, correlates of protection, and adverse reactions following vaccination in both young and older adults.

Females develop higher antibody responses, experience more adverse reactions to influenza vaccines, and show greater vaccine efficacy than males. Despite greater vaccine efficacy in females, both young and older females are often less likely to accept influenza vaccines than their male counterparts. Identification of the biological mechanisms, including the hormones and genes, that underlie differential responses to vaccination is necessary.

We propose that vaccines should be matched to an individual's biological sex, which could involve systematically tailoring diverse types of FDA-approved influenza vaccines separately for males and females. One goal for vaccines designed to protect against influenza and even other infectious diseases should be to increase the correlates of protection in males and reduce adverse reactions in females in an effort to increase acceptance and vaccine-induced protection in both sexes.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4157517/

Also:

https://pubmed.ncbi.nlm.nih.gov/33916167/#&gid=article-figures&pid=figure-1-uid-0

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8037587/table/jcm-10-01441-t001/?report=objectonly

The fact that there are indeed important differences in human male & female immune function, myriad areas of physiology generally, and in vaccine responses has been born out by the COVID-19 pandemic. Males across all age groups are much more likely to die of COVID-19 than females, and the greater the age the greater the sex disparity. Amongst people age 85 and up, men who contract the virus have died at 3.17 times the rate than women who've gotten COVID. And as most posters and readers here know, the vaccine is having different and unanticipated impacts on women than on men.

https://www.wavy.com/covid-19-vaccine/covid-19-vaccine-may-impact-women-differently/

https://www.usatoday.com/story/news/health/2021/04/10/covid-vaccine-women-report-more-side-effects-than-men-heres-why/7139366002/