Neither are particularly realistic enough to warrant distinction despite Marvel being the default answer. That said, it is possible to make a credible argument that DC is more realistic in the areas you've listed.
In terms of science, let's look at the origins of the comparable pantheons of their most popular characters: Superman, Batman, Wonder Woman, Flash, and Green Lantern as compared with Spider-Man, Wolverine, Iron Man, Captain America, Thor, and we'll toss in Hulk for good measure. One way to gauge realism is against how much suspension of disbelief a reader must engage in to accept the fiction. Thor and WW both introduce mythological magic so the field is even there. At which point, the underlying origin of all Marvel characters becomes apparent... human science... an accident for Parker and Banner, singular genius for Stark and Rogers, and a mad scientist for Logan['s blades]. Flash has ostensibly the same type of origin and Batman is just a mundane vigilante with all the same action-hero efficacy tropes that they all are subject to. So it falls to distinguishing human science versus alien science found in GL and Superman.
Here's the thing. Human science is mundane. We know what it is, how it works, and can form reasonable expectations for it. The idea that accidents involving mere human science results in Spidey, Hulk, Daredevil, etc. or that anyone like Tony exists clashes directly against our real world expectations for science. That's arguably why Flash has spent the better part of the last 20 years with an updated deterministic extra-dimensional origin instead of just spilled chemicals... or why Spider-Man had his origin updated to include magic... or why Tony's suit needs upgrading to keep up with contemporary times, expectations, and suspension of disbelief. By contrast, if you accept the existence of aliens- something you must do in either Universe- it is far easier to put aside your expectations because, really, how can you say what an advanced alien science or biology may or may not be capable of? It's fantasy either way, to be sure, but by mixing the mundane Marvel adds a heightened level of disbelief to be suspended. It is, in a sense, harder to believe in a fire-breathing house cat than it is a fire-breathing dragon. Don't get me started on the gap between our understanding of mutation and the Marvel's interpretation of it.
In terms of geopolitics, Marvel should be admired for creating more fictional nations of note to give their Universe a greater international feel, but at the same time that's where they run up against the disbelief. At Marvel, the fictional nations are incredibly notable, powerful, and significant. Genosha, Wakanda, Latveria, etc. are all significant set pieces... but they don't play out realistically. If Wakanda had a monopoly on a vital resource to the global market it's effect and place on global finance would be far more significant. If Latveria persistently threatened the world in one as cynical as Marvel's why has war been off the table when nations have gone through it for far less and with motives which would not be as transparent or as justifiable here. By contrast, the DC universe takes a more optimistic approach to geopolitics which is rather in line with reality (that is, despite doomsday fears it never quite arrives)... the nations that are created tend to be small and struggling nations without global impact but which act as stages for geopolitical parables to play out such as Bialya or Kahndaq or Pokolistan. They are "realistically irrelevant" as horrible as that sounds.
In terms of social interaction, I'm not exactly sure what this means... but in terms of how civilians view heroes both ways are probable- the public is just as prone to Romanticism (of political figures, celebrities, or corporations) as it is to fear and prejudice. I'd argue the Marvel Universe is a bit stuck in a time warp with respect to the lack of mutant rights progress. Obviously America isn't the most progressive nation but we're better than many places and certainly better than portrayed in the typical Marvel book. Crime in both universes, particularly violent crimes and robberies, is off-the-charts unrealistic but given the relative scope of powers, you run up against that wall of disbelief far more with the street-level popular Marvel characters than the larger-threat DC characters. Between the characters themselves it's much harder to justify the loose, temporary, and geographically nonsensical affiliations of teams like the New Avengers particularly considering their varying stances on things like lethal force. Why is Spider-Man on any team, really? You could level the same argument at Batman but his bankroll is really all the answer you need. Why the density of heroes in NYC? When the JLA each are guardians of their cities and literally watch over the planet from above... their loose affiliation making sense for tasks requiring their combined attention... moreover with legacies / families / etc. stand ins can be sent to meet the role as necessary... the dynamics are more obviously utilitarian. Finally, if in terms of personal character, the issue of paragon is often raised... but if that's the case really what are Steve or Peter's character flaws? I suspect that if you dig deep enough to find them in those two, they would be just as present in any of the DC Pantheon.
But this is all nit picky semantic type distinctions for two universes that are both ostensibly unreal to the same degree.
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