I think originally, the difference was how the Superheroes in each comic got started.
DC was making HEROES with epic stories...or, icons that kids could look up to. These were sort of like Heroes beyond belief that did extraordinary things.
DC was still making these types of Comic books when Marvel started up. DC's heroes at the time were supposed to exemplify heroic good, being larger than life and in some ways inspirational to the young readers that read them.
On the otherhand, Marvel said...what if we made these characters more relatable. Rather than have icons for the kids to look up to, have characters which they can relate to. Thus, most Marvel characters have problems relatable in some way to how kids in the 60s and early 70s may have had to deal with. There is poverty, racism, discrimination, disability, emotional problems, and various other things that people may have had in real life.
I'd say in the 60s and 70s the Marvel characters were definitely more relatable because that's how they were designed and it was a different philosophy than what DC and some other comics were having.
This changed in the 80s. Marvel, rather than staying relevant to kids, started to become more of a soap opera type idea which you followed from month to month. I'm not sure why this change occurred, but now it wasn't really dealing with the problems which limited them before, though they still had problems...you were now wondering who was Jean Grey going to end up with, who was Peter Parker dating and would he have heartbreak in a month or two, could he keep that relationship going without having major drama...etc..etc...etc.
DC at the same time moved to a darker attitude around the mid-80s. The Characters were no longer such perfect icons of heroic fantasy, but rather flawed dynamics which had weaknesses that were constantly explored whether that was some physical weakness, emotional or other such weakness. It was comparing and contrasting what MADE them heroes rather than that they just WERE heroes. It was showing that in many of the comics the Villains were actually very similar to the Hero of the comicbook, but it was the difference of CHARACTER that made the hero a hero and a villain the villain.
This is sort of the dynamic that we have today and that they are tryigng to recreate in the movies. For DC, I'm not sure they have been as successful in some ways with the modern DC MCU, though I think Nolan did a GREAT series of Batman films that examines that exact dynamic of DC comics from the 80s and 90s. It's that which appeals to the parents of kids today because those are the DC heroes they grew up with.
Meanwhile, in Marvel most villains (with the exception of Thanos) only lasted a movie, but you don't keep watching the movies for the metaplot of Thanos...it's more of how will Captain America deal with the modern world with his old fashioned habits...Will Tony Stark EVER pop the question to Pepper Potts and live happily ever after...will Thor ever make up and be good brothers with Loki? In this, I think Marvel has done a better job at recreating the Marvel comic dynamics of the 80s and 90s than DC has recently.
However, comicbooks have moved on (no idea if the current ideas will be accepted, as the sales are down quite a bit from earlier decades). Marvel has moved more to interpersonal conflicts now, where the conflict is not so much a soap opera (it's still there though) but one where the exploration of can a hero also be a villain, or can one hero be the villain of another hero at the same time, can we let the privileges we have be the same things that are making it harder for others in life?
DC has, on the otherhand tried to make their comics more akin to a cross between Marvel of the 90s with more of a soap opera feel at times and a combination of more relatable characters with a bigger focus on personal lives rather than heroics.
Perhaps in 30 years the Comic Book movies will also reflect these current trends rather than how they try to reflect the trends of the 80s and 90s that they try to recreate today.
