it depends on which version of the Avengers and the Justice League you're talking about. both teams have changed over time, Avengers getting new members and losing a lot, and same with the Justice League.
but lets say we're using these teams
Avengers - Iron Man, Captain America, Hulk, Hawk Eye, Black Widow, Thor, Scarlet Witch, Quick Silver, and Spider-Man
Justice League - Batman, Super Man, Cyborg, Green Lantern, Aquaman, Wonder Woman, Green Arrow, and the Flash
already, Avengers have an upper hand with a magic user, being Scarlet Witch, as most of the Justice League members are vulnriable to magic, like Super Man. Iron Man has his mark 50 suit, which is basically remoldable to his whim for the situation at hand. Thor is a god, now fitted with Storm Hammer, Hulk is almost unkillible, Hawk Eye, is a goods marksman. Black Widow, though not the best, can hold herself well against some of the members, i say. Quick Silver is extremely fast, and Spider-Man has a load of webs to use for the job, and can be creative too against them
Batman has a large arrey of tools, Superman's powerful, Green Lantern can basically make anything, Cyborg is a walking machine gun, Green Arrow is a marksman. Wonder Women has a lot of powers many don't know about, Aqua an has, well, the sea creatues, and the Flash is super fast
honestly, though, in my opinion, i'd say the Avengers, in this case, would win, because of Scarlet Witch