A few basic observations out of the way: no one at any point ever sat down with the intention of creating a fictional entity called "the Marvel Universe," or "the DC Universe." These fictions were constructed over the course of many years of seemingly accidental and slow-moving accretion, with numerous separately conceived individual pieces being fit together in haphazard fashion. No comics universe that was conceived as a holistic unit from its outset has ever survived past a few years from the moment of its origin. Effective fictional universes arise from the union of individually popular properties whose connection brings some form of benefit either real or imagined to future iterations of the properties in question: the universe itself cannot be a selling point unless people already care about the stars in the firmament. An argument can also be made, under this principle, that the very idea of a large multifaceted superhero universe works against the purity and strengths of original character concepts, and that in many notable cases the leavening effect of superhero continuity actively dampens the specific virtues of many properties. Captain Marvel is the best example of this, but the argument could be made that any superhero created before the mid-60s suffers somewhat from having been retroactively shoehorned into a larger context against the wills of their creators.
But with that said, shared universes have been the norm in superhero comics for almost five decades.
I understand that many readers find many of the conventions and expectations of shared universe storytelling to be, at best, superfluous, and at worst onerous. For someone such as myself who grew up appreciating these universes as living, breathing entities, they cannot but seem inextricable from my understanding and enjoyment of superhero comics. A strong universe-wide continuity does not necessarily have to become a blind by which bad storytelling is excused under the auspices of straitjacketed continuity - although this certainly happens quite often, there is also much to be said in favor of the synergy and frisson created by the syncretic accumulation of decades worth of abstruse detail and extraneous mythology.
I have always approached the respective comics universes in terms of the distinctive registers imparted by their basic mythologies. These mythologies that reveal the overriding tone and thema for their respective universes.
DC is predicated on essentially conservative notions of science fiction and fantasy that begin with the creation of the universe by a giant divine hand and proceeds onwards to the establishment of the oldest race of beings in the universe as a conglomeration of blue-skinned bureaucratic dwarves. Krona, the archetypal villain who transgresses against the natural laws of the universe and thereby creates evil, is a mustachioed villain straight out of classic Hollywood. There are numerous all-powerful patriarchs in the Judeo-Christian mold - Shazam, Allfather - who define the rules of engagement for mortal adventurers. One of the most powerful figures is the literal embodiment of the Judeo-Christian God's spirit of vengeance and retribution. As a result of the existence of the Spectre and his compeers, the existence of God is often assumed even by characters who have no direct contact with Heaven or Hell. Heaven and Hell do both exist, and not just in Vertigo: Superman has been to Hell and Batman has been to Heaven, where he's even met his dead parents at the pearly gates.
Marvel is a far more dangerous place in which to live. There is no God in the Marvel Universe: the various levels and permutations of mystic and cosmic potentates is amorphous and vaguely defined. You've got the Celestials and the Watchers and above them Eternity and Death (and Galactus, sort of) and above them the Living Tribunal, and above him the One-Above-All, who has himself been contextualized by the appearance of beings such as Nemesis (although her existence, contingent on the Ultraverse, is possibly not canonical and will probably never be referenced again), the Beyonder (in his original, pre FF #319 incarnation) and the Heart of the Universe (Marvel Universe: The End). It is important to note that the few times when explicitly Judeo-Christian concepts have made overt appearances in Marvel books, these concepts have been handled very gingerly: Dr. Strange summoned the power of Yahweh in a battle with Dracula, which had the effect of placing the Judeo-Christian God somewhere along the axis of Agamotto and Denak as higher powers whose authority could be evoked as necessary. Jesus - or a remarkable facsimile thereof - showed up in an early issue of Ghost RIder, but again, it was hardly definitive, and there's little in Marvel mythology (other than their desire not to offend huge swaths of their readership) to say that Jesus was any less or more "real" or "divine" than Thor or Hercules. (It should be noted that, while we're on the subject, Thor and Hercules and all the gods of Marvel are usually defined as kinds of aliens.)
No, the overriding theme of the Marvel cosmogony is not belief in a higher power, but ruthless change and constant interference. Human evolution on Earth is, after all, not the result of blind selection for useful traits spread over millions of years, but the result of tampering with the human gene pool on the part of 500 foot tall space gods who planted the seeds of genetic diversity within selected specimens of proto-man. This occurred only after millions of years of conflict between the elder gods Set, Cthon and Gaia eventually secured a place for mammals on the evolutionary ladder after the mass extinction of the dinosaurs. This is not even to mention the genetic experiments of the Kree, or the black monolith from 2001 which showed up at various points in human development - that's canon!
The point is not to debate which universe has the weirdest, most funky science-fiction / fantasy origins - that's a contest that could go on indefinitely. Rather, if you look at Marvel vs. DC, both universes - as discrete fictional entities - are predicated on certain presuppositions. DC is predicated on a universe constructed around something we vaguely recognize as Judeo-Christian mythology, with God and Satan and their respective emissaries interacting with the world. You can say that your story has nothing to do with the Spectre or Neron or Zauriel, but one of the greatest strengths and most severe limitations of this form of storytelling is that regardless of how gritty and grounded Batman may be, he has personally been to Heaven and seen the birth of the universe.
Likewise, if you're reading a story about the Punisher killing drug runners, it is impossible to forget the fact that the Punisher - Frank Castle, non-mutant, normal human homo sapiens - is the result of untold generations of selective breeding on the part of space monsters, magic earth mothers and blue Kree. The Punisher lives on the same world where Conan fought Kulan Gath during the Hyborian AGe and a talking duck named Howard roams the streets of Cleveland. Personally, I love that.