To me The Avengers is vastly superior to The First Avenger.
I think it comes down to how people view AOU. If you thought it was a good or great movie Avengers wins this argument. If you thought it was a bad or Average movie Cap wins.
AOU is a very decisive movie for fans and it seems to be the tipping point for this comparison.
I did a different comparison. I think the Avengers is better than TFA. But if TFA is the least of the Cap Trilogy and AOU is the least of the the current Avengers trilogy, then I would give the nod to Cap.
TFA < TA
TWS > AOU
It depends on whether you thought IW was better than CW.
I think we can all just agree that the true winners of this "battle" are The Russo Brothers.
TWS, CW and IW is an impressive 3 set of movies and in comparison to other directors?
Michael Vaughn - Stardust, Kingsman 1 & 2, Kick Ass & X-Men: First Class
Bryan Singer - X-Men, X2, Superman Returns, DOFP & Apocalypse
Zack Snyder - 300, MOS, BvS, Watchmen and JL
Josh Whedon - Avengers, AOU & JL
Guillermo del Toro - Blade 2, Hellboy & Hellboy 2
Sam Raimi - Spider-Man, Spider-Man 2 & Spider-Man 3
Russo Brothers - TWS, CW, Avengers 3
Christopher Nolan - TDKT
James Gunn - GOTG Trilogy*
I know most people would still pick Nolan, but I think the argument can be made even if their movies aren't part of a trilogy and if Avengers 4 is equal to better than IW, even more so?