How close the fight is depends on which era and who is a member, but I'd lean towards the JLA winning, regardless.
1) As the only one able to travel through time under his own power, The Flash is pretty much the fastest speedster in comics. Even when he was depicted in an homage in Marvel Comics as the amnesiac "Buried Alien"- as I recall, he had died or was thought dead in DC Comics at the time- he beat all of the speedsters in the Marvel Universe in a foot race in which they all had a head start.
2) Batman- psychotically- has a plan to defeat any meta human of which he is aware. As a problem solver, Tony Stark is his intellectual equal or superior, but he's not driven quite the same way.
3) At the peak of his power, not only could Superman travel through time himself, he was so strong he was capable of moving whole planets. While there is no known upper limit to The Hulk's strength, there's a delay built into his ramping up based on his temper. Even if you add Thor, Hercules, Iron Man, Wonder Man and The Vision to the Avengers lineup, the JLA can basically counter with Wonder Woman, the Martian Manhunter and Green Lantern.
When you get to the others, it's kind of a wash- Hawkeye vs Green Arrow, Atom vs Ant-Man/Giant-man/Yellowjacket, Scarlet Witch vs Zatanna...
So...it kind of becomes a "who shoots first, wins" showdown, with the JLA having the edge, IMHO.