I didn't mean "statistically significant" or anything otherwise technical.

This is the data I pulled [0] (apologies to mobile users for the formatting, it's TSV):

COVID19 VACCINE (COVID19) 8,507
DIPHTHERIA AND TETANUS TOXOIDS ACELLULAR PERTUSSIS POLIOVIRUS INACTIVATED HAEMOPHILUS INFLUENZA B AND HEPATITIS B VACCINE (HEXAVAX) (6VAX-F) 29
DIPHTHERIA AND TETANUS TOXOIDS AND ACELLULAR PERTUSSIS VACCINE + HEPATITIS B + INACTIVATED POLIOVIRUS VACCINE (DTAPHEPBIP) 2,247
DIPHTHERIA/TETANUS/PERTUSSIS/HEPATITIS B (DTPHEP) 8
HEPATITIS A AND HEPATITIS B VACCINE (HEPAB) 256
HEPATITIS B VACCINE (HEP) 5,991

With the query criteria:

Serious: Yes
State / Territory: The United States/Territories/Unknown
Vaccine Products: COVID19 VACCINE (COVID19); DIPHTHERIA AND TETANUS TOXOIDS ACELLULAR PERTUSSIS POLIOVIRUS INACTIVATED HAEMOPHILUS INFLUENZA B AND HEPATITIS B VACCINE (HEXAVAX) (6VAX-F); DIPHTHERIA AND TETANUS TOXOIDS AND ACELLULAR PERTUSSIS VACCINE + HEPATITIS B + INACTIVATED POLIOVIRUS VACCINE (DTAPHEPBIP); DIPHTHERIA/TETANUS/PERTUSSIS/HEPATITIS B (DTPHEP); HEPATITIS A AND HEPATITIS B VACCINE (HEPAB); HEPATITIS B VACCINE (HEP)
Group By: Vaccine Type
Show Totals: True
Show Zero Values: True

It looks like ~130m people in the USA have received at least one dose of any Covid-19 vaccine [1]. It's hard to pin down a number of Hep B vaccinations as of 2021, but it looks like about ~70m people had been vaccinated as of 2002 [2]. 91-93% of newborns in the USA have been vaccinated for Hep B every year since then [3], and I very roughly guessed that 3.5m babies are born every year in the USA [4]; at 91% of 3.5m over 20 years, that's very very very roughly 64m people vaccinated against Hep B since 2002.

So there have (maybe) been at least as many Hep B vaccines administered as Covid vaccines, and there have been 2500 more adverse events for Covid-19 vaccines than for Hep B vaccines. The difference is smaller than I remembered, so I regret saying it's "significant".

That said, we can compute 99% confidence intervals [5] for both of these (in R):

library(binom)
(cis <- binom.confint(
x = c(8500, 6000),
n = c(130000000, 134000000),
conf.level = 0.99,
methods = "agresti-coull"
))
# method x n mean lower upper
# 1 agresti-coull 8500 1.30e+08 6.538462e-05 6.358307e-05 6.723719e-05
# 2 agresti-coull 6000 1.34e+08 4.477612e-05 4.331152e-05 4.629023e-05

So yeah, the difference between 4.5 per 100k and 6.5 per 100k is statistically significant. The two estimated distributions basically don't overlap at all (which you can confirm by looking at the percentiles).

You can add as many 9s as you want to the confidence interval size, and you will get basically the same result.

But I don't know if this is considered a medically significant effect size.

Edit: This is a back-of-the-envelope result. Please do not take it very seriously.

[0]: United States Department of Health and Human Services (DHHS), Public Health Service (PHS), Centers for Disease Control (CDC) / Food and Drug Administration (FDA), Vaccine Adverse Event Reporting System (VAERS) 1990 - 4/10/2021, CDC WONDER On-line Database. Accessed at http://wonder.cdc.gov/vaers.html on Apr 21, 2021 1:31:17 PM

[1]: https://www.usatoday.com/in-depth/graphics/2021/01/14/covid-...

[2]: https://www.cdc.gov/mmwr/preview/mmwrhtml/mm5125a3.htm

[3]: https://apps.who.int/gho/data/view.main.80300?lang=en

[4]: https://www.cdc.gov/nchs/fastats/births.htm

[5]: https://stats.stackexchange.com/a/423964/36229