The quiet moment with the combined pair of superteams, in which there's reconciliation, reflection, and in a tearjerking moment, Hal Jordan and Barry Allen (both deceased at the time of the series) talk about missing the opportunity to have a picnic with their wives together, topped off with a talk between Superman and Captain America in which they reveal their private fears; Superman worries the JLA is doing too much for mankind, stifling its growth, while Cap worries that the Avengers aren't doing enough. They acknowledge just before returning to their own respective dimensions that it doesn't matter in the end, so long as they fight the good fight.
Green Arrow, thinking Hawkeye has been killed, takes his arrows and vows to make each one count. Throughout the series, their massive egos had clashed over who was the better archer.
Speaking of which, Hawkeye is also now the only Marvel character to have been officially inducted into the Justice League of America.
During the final battle with the various enemies gathered by Krona against the two joined teams. After Green Arrow apparently died in action, Wonder Woman ordered the rest of the heroes to press the attack, while she would take up the rear and fight off anything that might attack them from behind. As she prepared to face Surtur, her mother Hippolyta (the Golden Age Wonder Woman) and She-Hulk announce that they will fight at Diana's side. Shulkie's comment was especially in-character (doubling as CMoF):
She-Hulk: Yo, Star-shorts! Figured that you'd be getting bored, so I thought I'd hang with you. We can talk girl-talk. Y'know, butt-kicking, name-taking, like that.
Wonder Woman (Hippolyta): Exactly. And I will stand by your side too, daughter.
Wonder Woman (Diana): I... I'm honored... And very thankful... Onward, then... For Gaia's glory!
Even more Heartwarming in that Hippolyta was dead at the time, giving Wonder Woman one last time to be with her mother.
After the final battle, Superman discovers that he can't lift Thor's hammer anymore. Thor explains that Odin temporarily suspended the enchantment in order to let Superman wield it. But then he adds this:
Thor: Perhaps it was but briefly... but it was in good hands.
Barry Allen & Hal Jordan, commenting that the Flash & Green Lantern legacies are in good hands with Wally West & Kyle Rayner.
Seeing Kismet and Eternity, the physical embodiment's of the DC and Marvel universes respectively, fall in love is a literal heartwarming moment between the two universes. Seeing them pulled apart is equally heartbreaking.
On a meta level, this symbolizes the respect and friendship that DC and Marvel hold for each other, regardless of their rivalries. After all, if the two big names in superhero comics didn't love each other, crossovers like this could never exist.