The common perception is that Packard was the best selling luxury brand until Cadillac finally topped them in the post war era, consistently so starting in 1950 (also for one year in 1947). But that’s by brand, and once Packard expanded its range downmarket into the mid-price field with the 120 in 1935, it was no longer exclusively a luxury brand. Which explains this ad, where Cadillac points out that they’ve been the best selling car over $1500 for a number of years. And that they actually sell almost as many cars above that price point than all the competitors combined.
So the common myth that Cadillac was somehow playing second fiddle to Packard prior to 1950 or so doesn’t exactly stand up to the facts. Of course Cadillac didn’t have to go down market after the start of the Depression; it had the cheaper LaSalle, and there were GM’s mid-premium brands to take up the battle with Packard’s 120 and such.