This is not my experience at all. First class is better than business class on international (and domestic, of course, though relatively few domestic routes have true three cabin service [counting all the slightly different economy levels as one cabin]).
Frontier doesn't have a business class nor long haul international flights (they are an ultra-low cost carrier).
Delta calls their highest tier "Delta One" their business class offering. It's mostly available in mid & long haul international flights, though there are a few select domestic routes with it IIRC. A tier below is First, which is available for both domestic and international flights. https://en.wikipedia.org/wiki/Delta_Air_Lines#Cabin:~:text=D...
United's highest is called "Polaris", representing their international business class. Confusingly, they have "United First and United Business" as the next class. I.e. it's the same class but on domestic flights they call it "United First" and on international flights the same seat would be sold as "United Business" despite having Polaris for that already. Regardless of that oddity, the First class can't be higher than itself named Business class even compared directly instead of with the actual business class Polaris - it's the same seat. https://en.wikipedia.org/wiki/United_Airlines#Cabins:~:text=....
Other airlines label and order things differently of course. E.g. American has Flagship First above Flagship Business above First/Business (shared much like United on that 3rd class) and maybe that's where your experience is. To my knowledge though, no such airlines operate the ATL<->SFO route originally described though.
Here are airlines offering three-cabin services on a single aircraft where First is the highest tier:
Air France - La Première (First), Business, Economy
American Airlines - First, Business, Economy
Cathay Pacific - First, Business, Economy
Emirates - First Class suites, Business Class, and Economy
Etihad - First Class private suites, Business, Economy
Japan Airlines - First, Business, Economy
Lufthansa - First, Business, Economy
Again, hbosch said ATL<->SFO... and you aren't going to be flying Air France or Japan Airlines for that route. My list, as far as I'm aware, was exhaustive for that route. It was not a cherry picked search of airlines which do it that way or global claim of what all other airlines do, only a response to the particular claim. On other routes/airlines the statement could, or rather "would", certainly have been true. Honestly, I think those airlines have it the right way around, but, having flown the exact route and the same airlines internationally, it did not match my experience for the route - which agreed with the labeling for all airlines for that route according to the links above. Unless, perhaps I'm missing that American or similar does actually have a ATL<->SFO to be compared with?
