Ok, one thing you have to think about what the the enemies of both sides are ,
JLA enemies darkseid-Stronger than any member of the avengers or justice league , and is immortal and therefore undefeatable
Doomsday,which is strong enough to defeat superman.
Lex Luthor- not very strong but has the brains and the money to destroy the justice league
Criminal syndicate of america,
and many more.
Thats all the enemies that I know but the avengers most likely have a lot more than that.
Justice League members
Jon Jon'zz (Martian Manhunter)
JLA has more but the avengers have Hulk , But one thing that you need to have in mind is that they bought fight for the same goal
rotect earth, so they would most likely team up and fight the bad guys(that would make an epic movie).But if they would fight fight each other I would go with the Justice League winnning as they have the intelligence and teamwork to do it.I'm not saying that the avengers dont have teamwork or good leadership, its just because some of the avengers dont get along with other members.It would end up with losses on both sides too.JLA has way more powerful enemies than the avengers do and they still succeed .