According to MyGermanSheperd.org:
In the USA alone there are about 78.2 million dogs, and about 4.6% of all AKC registered dogs are German Shepherds. This gives over 3.5 million German Shepherd dogs in the USA alone!
Meanwhile, according to Dog Bite Law:
There are approximately 4.5 million pit bulls in the United States, making up approximately 5.8% of the country's canine population.
(Merritt Clifton, Breed Survey 2019: More Puppies Yet Fewer Homes for Pit Bulls, https://www.animals24-7.org/2019/07/09/breed-survey-2019-more-puppies-yet-fewer-homes-for-pit-bulls/.)
for their data. That page say more precisely
Among the estimated 78 million dogs in the U.S. as of July 2019, about 5.8%, or about 4.5 million, appear to be pit bulls or pit mixes. This is slightly more than one dog in twenty.
It surprises me that there are more Pit bulls than German Shepherds.
Note: The term Pit bull is broader in the United States than other countries. Animal Foundation explain:
Today there are at least five breeds of dogs that are commonly misidentified and lumped into the category of the pitbull-type dogs: the English bull terrier, the American bulldog, the boxer, the American pit bull terrier and the American Staffordshire terrier.
Ideally, I am looking for an answer that uses either the United Kennel Club or American Dog Breeder's Association [which is dedicated to the American Pit Bull Terrier] definitions.
I first posted this question at Pets but was recommended to post it here instead.
Update: The reason I ask this question, is that I want to related the numbers in this Wikipedia article https://en.wikipedia.org/wiki/List_of_fatal_dog_attacks_in_the_United_States to the total population of each breed.