The Leagues biggest disadvantage is that they only have one flier.
Though if they head for solid structures or go under ground they may be able to minimize the Avengers flight advantage. Remember per the OP the Avengers are hunting the LXG. So the League can pick the playing field, to some degree.
Also if we factor in personalities. Thor is likely going to hesitate when it come to going full force or even attacking Mina. As it seemed he believed in some form of chivalry when of sound mind. Though her turning all fangy or into a flock of bats might just change his opinion quick.
On the ground things are fairer. As Nemo, Quartermain, Sawyer, Gray, and Hyde are going to be a good match for Hawk Eye, Hulk, Black Widow, and Cap.
While the knee-jerk response seems to be that Barton snipes every body, it is ignoring the fat that both Sawyer and Quartermain pulled off some damn impressive shots of their own.
Sawyer should be able to tangle with Barton, he may not be as accurate, but he has a higher rate of fire. Quartermain can square off with Widow. Leaving either the combination of Gray and Hyde or Nemo and Hyde to take on Hulk and the remainder to go after Rogers.
Or multiple version their of. Point is its the air battle that really kills the League. If this took place in the Fantoms fortress or a Helicarrier I'd like their chances better. Not saying the LXG would win under those conditions, just that they'd have a better chance.
All in all though. While I don't think its gonna be as easy for the Avengers as others think. I'd still give the win to them.