From the DC wikia:

All-American Publications is one of three American comic book companies that combined to form the modern-day DC Comics, one of the world's two largest comics publishers. Superheroes created for All-American include the original Atom, Flash, Green Lantern, Hawkman, and Wonder Woman, all in the 1940s Golden Age of comic books. Max Gaines, future founder of EC Comics, formed All-American Publications in 1938 after successfully seeking funding from Harry Donenfeld, CEO of both National Allied Publications (publisher of Action Comics and other titles) and sister company Detective Comics (publisher of that namesake comic book).

While All-American, at 225 Lafayette Street in Manhattan, was physically separated from DC's office space uptown at 480 Lexington Avenue, it used the informal "DC" logo on most of its covers for distribution and marketing reasons. (The DC logo at the time was also used for National's unofficial branding, capitalizing on the success of Batman in Detective Comics.) In 1944, Gaines let Liebowitz buy him out, keeping only Picture Stories from the Bible as the foundation of his own new company, EC. "Liebowitz promptly orchestrated the merger of All-American and Detective Comics into National Comics. Next he took charge of organizing National Comics, Independent News, and their affiliated firms into a single corporate entity, National Periodical Publications".

Suppose this never happened? What if All-American continued onward publishing its own material without being merged together? What would the separate companies look like?

(Let's suppose, just for the sake of argument, that neither company goes out of business and they continue publishing in some manner.)

Well it'd be safe to say that Marvel would be the top dog. I'd like to think both companies would survive, especially considering the strength of Batman, Superman, Flash and GL as character IMHO. However, if you look at all the different comic companies of that era, it's not easy to assume that. I know Max Mercury, Shazam, and Blue Beetle (along with many more) were all originally owned by other companies, each were bought out by DC or its predecessors, or won via court. If you look at Alex Ross' Project Superpowers, each of those characters were originally owned by Golden Age comic companies who each stopped publishing eventually, and thus all the characters used are no longer under copyright. One could suggest that in your suggested scenario, some characters currently considered as DC greats would be published in a Dynamite Entertainment team-up series. The positives of that, IMHO, although very few would be that we'd perhaps see even more of Ross' interpretations of classic characters, and that Wonder Woman would be less prominent in popular culture (I don't like her as a character).