JLA vs Avengers (See combatants)

JLA: 
Hawkman 
Plastic-Man 
Green Arrow 
Black Canary 
Vixen (Tantu totem-only using animal abilities) 
Aquaman (fully powered, 100% h2o levels but can't use his telepathy on his opponents) 
Mister Miracle 
 
versus: 
 
Avengers: 
Black Panther  (w /vibranium suit & pre-power up)\ 
Black Knight (Dane Whitman) 
Falcon 
She-Hulk 
Captain Britain (Kelsey Leigh) 
Mockingbird (Bobbi Morse) 
The Beast (Hank McCoy) 
 
Random battle takes place in the ruins of the old Avengers mansion. No BFR for either team. Fight until one team is left standing.

Aquaman solos

JL would take this team pretty easily. Hawkman, Plastic Man, and Aquaman are powerhouses in this contest. She-Hulk and Black Panther probably hold their own but the rest are in for it. 
 
Anyway I always thought of JL and Avengers as two entirely different concepts. JL is a team of powerhouses who can get by smashing and outpowering foes. Whereas the Avengers where more tactical. A lot of times the Avengers would have a roster with about 2 or 3 non powered heroes who relied on fighting prowess and stealth. JMO

Yeah, I was trying to use some random peeps that you don't see in a lot of battles. But I made the JLA  a bit too strong.