We deeply appreciate the concern of all you True Believers – but don’t worry about it, gang.
First, in Brave and the Bold #68, he has Batman become the Bat-Hulk… Hilariously, Lee then had a Stan’s Soapbox in late 1967 where he explained that they were going to stop calling DC Comics “Brand Echh,” except, of course, in the entire comic book series dedicated to calling DC Comics Brand Echh….
Similarly, the parade of Editors-in-Chief that followed Thomas in the 1970s were guys who worked for DC and Marvel, so it was hard for them to give DC much of a hard time (one of the harshest comics of the period was a Warlock issue where Jim Starlin viciously took down…Marvel).
At the turn of the century, though, Marvel gained a new Editor-in-Chief in Joe Quesda and a new Chief Operation Officer in Bill Jemas and they were more than willing to return to the days of the rivalry.
Much of the rivalry discussions have moved to comparing their movies to each other, but even there, it was only very recently that DC Entertainment got into the shared film universe phenomena, so there was not a whole lot of opportunities to contrast the two companies with each other.