Gwayne gave meaning to Criston's end.
Criston and his story helped Gwayne become the best version of himself.
(meta?).
Yeah, I know all the "what 30 days next to Criston did to Gwayne" stuff is just jokes. But seriously, I think a lot of people underestimate just how beneficial their journey together was for both of them.
Gwayne couldn't make Criston give up his desire to die, but it was their conversation about honor that sparked Criston's final breath. Even if in a distorted way, he actually listened to his comrade's words. And if before that Criston was aimlessly drifting with the flow waiting for death, afterward he was actively rushing toward it on HIS OWN terms. He knew he was destined to die, that nothing awaited him after, but he CHOSE how he wanted to go out. Criston didn't need saving - he needed meaning, and unintentionally, Gwayne gave him that.
As for Gwayne himself, he underwent a massive transformation - from a polished, arrogant knight carelessly strolling across an open field in search of entertainment amidst a war, into a more humble and hardened warrior who saw terrible things, yet didn't let them break him.
But his greatest growth is overcoming his own racial and class prejudices: whereas before he saw Criston as nothing more than a Dornish upstart who took his father's place, now Gwayne sees a human being with his own story and pain. Even if he'll never fully understand what it's like to be lowborn, he showed Criston more humanity than anyone else did. And you can see that it truly touched Criston, and when he told Gwayne he was grateful, that's exactly what he meant.
You could say that Gwayne gave Criston a sense of peace before his death - by being his loyal comrade, a supportive friend, an amusing storyteller (just look at Criston's smile; in his current state, making him smile is a real achievement), and someone who accepted Criston as he is, with all his sins and flaws. Gwayne was the first person who wanted to do something for Criston himself, and that meant a lot to the latter.
Criston and his story, in turn, opened Gwayne's eyes to the fact that the world isn't black and white, that knighthood is far from being about nobility, but about hard choices: between desire and duty, loyalty to the law and to the people you love. Criston Cole himself once viewed the Kingsguard as a ticket to a better life, but the exploitation of his body and his loyalty, his disillusionment, and his existential self-loathing bring to mind a line from a great TV show: "I died long before you were born, this is just a formality." Just like Criston died long before this war.
Addendum: I also want to emphasize that the differences in their reactions to the events at Rook's Rest don't make one stronger and the other weaker. This isn't the first war Criston has fought in, yet that didn't stop him from keeping his drive and idealism in the past. By the time the Dance of the Dragons began, Criston was already balancing on the edge due to his devastating self-loathing, but he was holding on for the people he loved. And seeing them ready to destroy each other - that is what broke him, not the dragons. A battle that was supposed to be a triumph turned into a personal tragedy for Criston, who was forced to helplessly watch brother kill brother.
What Aemond did, what happened to Aegon, his failure to protect his king - it all became a point of no return. No one, including the Dowager Queen (who he knows doesn't care about him), could have saved him from himself.
