Epistolary forms have such power to quickly express who a character is, and what they're all about. There are options with the epistolary form that you just don't have with simple prose; decisions to be made that will reveal an awful lot about the character writing the letter. To whom do they address their missives? How do they write? Are the letters private, or do they anticipate other readers?
The letters between Remus and Sirius are a delight to read. Partly because they are very funny, and very charming. There's very much a sense that they're showing off to each other a bit. Sirius is always a show-off of course, and everything about his writing yells LOOK AT ME I'M HILARIOUS AND FREQUENTLY NAKED, both the content and the presentation. Abuse of punctuation, the lot. But Moony's showing off too, albeit in a quieter and more detached way: showing off his vocabulary and wit and knowledge of fancy letter writing customs. They are clever boys trying to impress each other.
But also, we get moments like this, and they are much more telling (of Remus and Sirius' relationship) than any of the jokes about Sirius wanking over Remus' letters (though that he insists on writing letters alone in the garden is interesting):
How was yesterday? It was weird not to be there with you, we were thinking about you though. I was thinking. I hope you were okay. REST UP ALL RIGHT, don't do any calisthenics for a couple of days and no violent shagging!!
It's a postscript in a longer and sillier letter, but its position at the end only serves to underline its importance. It's no throwaway add-on. Note the standard punctuation. Sirius takes a break from talking about himself (of which he is very fond, bless his heart) and expresses his concern for Remus. And he specifically isolates his own concern from that of the others. I was thinking. But things have gotten a bit too serious now, so we get the jokes and punctuation!! Because feelings, (like the quiet) are booooorrriiiinnng!!!