In the final book of the series, when Harry Potter is about to face Voldemort, he takes out the resurrection stone and sees his parents, Sirius, and Remus. Lily and James were both wearing the same outfit they wore the night of their death. Therefore, we can conclude that they all appear how they did the night that each of them died.
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With that being said, Sirius Black and Remus Lupin appeared to be much younger. Harry stated that 'Sirius was tall and handsome and appeared much younger'. Lupin appeared much younger too and much less miserable with thick black hair.
So what does this all mean? Prisonersirius came to the conclusion that both of them died the same night as Lily and James. We're not totally convinced by this, but it's certainly an interesting point-of-view...