It isn't so much a headcanon but how I view them when I write.

Echoing what others are saying about introvert Sirius, I love that. I always imagine them being exactly who the other person needed at that point. During their school years, Sirius brought Remus out of his shell, turning him into the more-confident (but not cocky) sarcastic boy that I love. When Sirius was broken after prison, Remus was the calming voice, the person who settled him above anyone else. While he never forgets the invisible scars, Remus tries to heal them just as Sirius did for Remus at school.

Sirius always knew he was gay, and the posters of women were out of fear his mother would find out but also riling her up. Whereas Remus was conflicted, not knowing that he could like both boys and girls, because all he had been told is how dangerous being a werewolf is.

Sirius is fluent in french, but despises it where as Remus adores it. Remus self-teaches himself latin, but after fifth year and finding that both chocolate and Sirius are a huge distraction, doesn't continue with it.

Remus is a heavy sleeper who needs a lot of sleep, Sirius is a night owl who runs off very little sleep.