I hope the same. There's really no need for them to feel like they need to play catch up because
I think the cards are stacked in their favor right now. The MCU is for all intents and purposes done after Infinity Wars and on its way out. Many of their major characters will presumably be done, with their biggest name character from then on likely being Spider-Man. I don't feel many people will be interested in potentially seeing Bucky as Captain America, Ant-Man and the Wasp, Captain Marvel, and Dr. Strange by themselves as being the new cast of main characters.
The DCEU on the other hand, is just starting and all of their big name characters are still in play and will be for awhile, which are also arguably characters more widely popular than the MCU's main characters. I think people will have a greater interest in characters such as Batman, Superman and Wonder Woman than they will in the aforementioned new cast of main characters on the MCU side of things.