Universe Unlimited had the plus of having mixed the two universes very well. I mean, some things were ignored and caused some continuity/logical problems, but I did sit in there and fix some of those, at one point, at least to most people's satisfaction.
I think if you make a mixed game you have to accept two things: 1) you'll disappoint some people with any changes you make to fill in gaps or explain discrepancies; and 2) you'll have to shift the ambience and feel of both, if they're very different, until they can cohabitate.
For example, in the Marvel universe, mutants suffer a lot of persecution (let's ignore the fact that Average Joe and Jane seem to have a special radar and are always able to tell when someone is a mutant, and thus worthy of persectuion, and when they aren't, and thus worthy of trust because superheroes). Meanwhile, in DC, most metahumans (many of which are essentially 'DC's mutants' since it's basically just 'born with these powers randomly') are not.
So you pick one. Since Marvel's is a much more integral and important part of a lot of characters, I usually favor using that.
Other things are just fun to mix and match and see what you can do!
Namor does not rule Atlantis. He rules Lemuria! His people are an off-shoot of Atlanteans that left Atlantis centuries ago. They have a wary truce with Aquaman and Atlantis.
The Kree are descended from ancient Kryptonian explorers. It explains their higher physical powers, probably diluted (maybe they once lived with a yellow sun, but it's been millennia since then). (And hey, their naming conventions are very similar!)
The Nova Corps was an attempt by the Guardians of the Universe to create a new intergalactic police force when [x thing with the Lanterns] happened, but they ended up separating from the Guardians and now operate on a different scale than the lanterns (or whatever).
Quicksilver's mutant power allows him access to the Speed Force. (So many people hate this idea, and I don't know why, or care.)
The Celestials are responsible for [name any number of weird fucking things in the DC Universe, including even the Anti-Monitor].
Galactus and Mogo are totes frenemies and Ego constantly feels left out.