If you had to choose one word to describe the DCEU, it would probably be dark. But play that same game with the MCU, and the word you choose would most-likely be fun.
BvS is ultimately a very dour and depressing film. It casts two of the world's greatest superheroes as morose sadists who take themselves far too seriously. You have a Superman who has apparently forgotten to smile and a Batman who has to grunt and come up with "badass" lines like "Do you bleed?"
Civil War doesn't go down that route. Even though you've got superheroes fighting each other and a conflicted rooted in real-world concerns about power and how to monitor that power, there's still a lot of fun in these movies.
No matter how grim things get, there are still moments of levity to balance out the bleak. The interactions between the characters portray them as intelligent people with real concerns, but they also aren't afraid to diffuse the tension every now and then.
BvS makes the mistake of painting every single character with the same murky colors. There's almost no variance in the depictions of the characters. Even visually, the film is extremely dark and difficult to watch at times.
There needs to be a balance struck between the light and dark elements, and that's a lesson DC has yet to learn.