Long Ago and Far Away

I identify with both of them, but for different reasons.  As far as a preference goes, Moony is my favourite character in the whole Potter fandom.  I know his lycanthropy was at least originally meant to be an analogue for HIV-AIDS and wasn't there something about how people treat those with disabilities?

I have invisible disabilities and have first-hand experience of how differently people treat you once they know you have them so, in a way, it's almost inevitable that I'd identify most strongly with Remus.  Fanon, at least, tends to portray Remus as reticent and with self-esteem/self-worth issues (I am less convinced of their existence in the canon), and as I have self-esteem/self-worth issues it's another reason to identify with Remus.

The reasons I identify with Sirius mostly surround his obvious mental health issues.  I've never been framed for murder or unjustly imprisoned, but I have spent most of the last twenty years battling against major depression and it's damn clear (to me) that Sirius is at the very least badly depressed while he's trapped in Grimmauld Place.