Are we talking present day JLA roster vs. one or both of the present Avengers or just an all out slugfest between everyone who's ever been a member of either team? Regardless here's how i see it:
New Avengers go down to the JLA, as do the Mighty Avengers (but they hold there own a little better).
If the New and Mighty Avengers teamed up, JLA gets the loss. Sentry, Iron Man, and Strange is a pretty big feat especially with Ares of back-up...
Every JLA member versus every Avenger? I think the sheer number of Avengers could over power the League and then you take into account the volume of heavy hitter's they'd be packing: Hulk, Thor, Thunderstrike, Hercules, Namor, Dr. Strange, Sentry, Cap, Wolverine, Iron Man, War Machine, Ares, Vision... hot damn. JLA would be screwed hard and dirty...