This was just an idea a friend came up with; feel free to use it yourself. First of all, ask yourself: Does the universe I play have more of a Marvel or DC feel? Once you've answered that, here's the challenge: Take one of your already-existing characters, and adapt them to fit in the other universe.
For instance, my gaming group's primary hero-'verse has a very early '80s Marvel feel to it, with a splash of Dieselpunk for flavor. One of the characters I play is strongly influenced by Alan Moore's famous creation, Tom Strong (blend of gadgeteer and Indiana Jones-style adventurer). So his DC equivalent isn't as science-minded as the main one: rather, he's more of a blend of Nightwing and the Warlord (Travis Morgan). Still a world-travelling adventurer, with various skills he's picked up over the decades, but not as science-minded as his "brother".
So that's the idea: Determine if your character is more of a DC or Marvel, and create his other-verse equivalent. Have fun!