Avengers vs JLA. I have been a fan of Batman, Superman and Wonderwoman and the other JLA members for some time. However, I have been more of a fan of the Marvel world because of its unpredictability and more human characters with weakeness.
Although Superman is stronger than Thor. Thor has centuries of experience and quite honestly has mystical powers that Superman can't match. Also, one dimensional spin of the Hammer and no more Superman.
Batman vs Captain America. Captain America wins hands down. Sorry, but Cap is a pure fighter, stronger, faster and does what he has to to win. So does Batman, but in a straight fight, it goes to Captain America. Batman is a detective. DC has managed to upgrade his fighting skill over the years, but Captain America beats all fighting skills.
Green Arrow vs Hawkeye. It goes to Hawkeye. Both are equal on archery skills but, Hawkeye has arrows that can take out Thor and Captain America taught Hawkeye to fight. End of story.
Quicksilver vs Flash. I was so pissed that DC killed off the original Flash (silver age). I don't buy killing off someone then bringing them back as another person. But, the fight goes to Flash. He has rediculous speed. Quicksilver will be like he is standing still. However, if he slows down for an instant, the fight goes to Quicksilver. Again, Captain America taught Quicksilver how to fight.
Jon Jones vs Vision. Goes to Vision. He has basically Thor Strength and he can change density and he has fire from his eyes. The density change makes him dangerous to Jon. He can enter him and slowly solidify. Fight over.
Sub Mariner vs Aquaman. Sub Mariner has Thor like strength and gets stronger in water. Both are equal in water and Aqua life control abilities. Fight goes to Sub Mariner.
Wanda vs Wonder Woman. Your guess is as good as mine. Wanda's abilities make her the most dangerous Avenger. Wonder Woman is one of my all time favorites. Wonder Woman may be able to take Wanda out before she can use her powers. However, if Wanda gets going, watch out.
Ant Man/Wasp vs. The Atom. Equal sizes, fight goes to Ant Man. Captain America taught him to fight. However, I'm not sure about the Atom's powers.