JLA wins pretty handily. The dials go to eleven in DC. Superman himself is the last one standing and maybe one or two other JLA members. Can't say for sure which ones because it depends on who they match-up against but Superman beats anyone on Avengers without much difficulty except for Hulk and Thor. They would make him work for it but he still beats either one of them in the end. Then he can help out whoever needs it.
Just too much power on JLA for Avengers to deal with. Basically, everyone on Avengers except for Hulk, Thor, IM, and Vision is nothing more than a nuisance to the JLA. GL, WW, and especially MM would all beat IM without too much difficulty. Flash gives the Avengers all kinds of headaches by running interference for JLA.
Too late to edit my post. Just wanted to say that besides raw power, the speed on JLA is just too much. Superman and Flash (also WW and MM to a lesser extent) could easily take out half of the Avengers in the first few seconds. Diana could easily get the lasso around Hulk since she's much faster than him and he isn't breaking it. Please don't even bring up Bizarro breaking it. That's not canon...Then there's MM telepathy for Avengers to have to deal with too. Just too many ways for JLA to win.