Kyle: Okay, The Avengers won this round ...
... And they totally won at the box office this week. But there still were several big arguments that they could have used on NRA.
Right off the bat, Chris should have jumped all over my first big comment. While The Justice League has a semblance of exclusivity that made them more of a team, Chris could have argued that the Avengers' open-enrollment is much more heroic. After all, with a revolving line-up the Avengers have a greater chance of resolving a situation with the appropriate skill-set.
How many instances would call for Aquaman? Very few. But any number of situations could be solved by whichever random, C-grade hero got the latest internship at the Avengers mansion.
And if there's one thing I messed up on, it's this idea that a group of living gods plus Batman are a better team than an endless horde of extraordinary mortals with personal demons and issues. If there's one thing that Greek myth has taught us, it's that all-powerful folks with mommy issues and sexual dysfunction make for some crappy teamwork. Does that sounds like the same crap that would happen with Spider-Man or Wolverine present? No? How about Superman or Green Lantern?
Oh, that's right. That's how Parallax happened.
And one thing that we didn't even mention: Would you rather live as a citizen under the protection of the Avengers, or the Justice League? I'd rather have some semblance of protection from a highly organized group of sometimes-government-funded geniuses and good-hearted warriors rather than a lofty amalgamation of alien immigrants, power-crazy space cops, and regal muckety-mucks that see us as mere ants in a tube that must be tended to whenever they are bored.
Also the Avengers have a large group of world-threatening villains that have no personal stake in the heroes but a more global-scale threat. The DC universe is largely populated by petty villains that just want revenge or a balance of misfortune for the hero that gets their goat (like the Joker, or Lex Luthor). In the Marvel world, we have serious villains with serious plans and means to vaporize the whole planet, thus necessitating an big team-up (such as Thanos, or Galactus, or the Skrulls).
In the end, the Avengers are the heroes we really would need, but the Justice League is probably closer to what we would end up with, which might be the reason why people find them less fun.