For my part, Draconic is:
Not heavy on the sibilants per se, but diverse with them, meaning sounds that are considered one allophone in (essentially?) all human languages are treated as distinct sounds. Like how the Hawaiian transliteration of "Merry Christmas" is "Mele Kelikimaka," with "ch," "st," and "s" all cashing out as "k."
Definitely has some shades of Aztec, Russian, and Germanic weird consonant clusters. I imagine dragon lips are more mobile than most give them credit for, and thus expect a pretty large consonant inventory.
Heavy on long and back vowels, so not very similar to American English at all. Dragon breath is a voluminous thing, and being long-winded carries certain positive connotations in spoken language as a result.
Highly inflected...but full of abbreviations, even worse than Latin. There's a thorough case system, with some cases not normally found in Earth languages; likewise the conjugation system is more intricate and precise than many Earth languages, with more tenses, moods, and aspects.
Written with two scripts, Claw and Fire (or Breath). Claw script is, as the name implies, made with claw marks, and resembles cuneiform or the TES dragon script. Designed more for personal use and everyday stuff, and quite good for carving into stone. Much easier for mortals to read and translate--very much a feature rather than a bug. Fire/Breath script is cursive, based on the notion of being burned into something with fire (or the breath of a dragon, presumably at point-blank range so it can't spread out too far). Fire/Breath script is much more formal and fancy, it's for important documents, threatening your rivals, and generally communicating a "high draconic society" vibe.
Most Earth human listeners would find it almost but not quite sing-songy, due to the partial rhythm produced from alternating long and short vowels. The various flavors of sibilants are lost to most human ears, robbing it some of its subtlety, and the occasional harsh consonants cut through the long, flowing sounds. This has helped its status as a language of magic; the deep declension and conjugation systems make rhyme possible but not trivial, and the innate rhythm makes it sound poem-like to us even in ordinary prose (after all, Sublime Rhyme is a thing!) The preciseness of its verbs and cases lends it to being very specific about plans and designs, which also lends it to the discussion of military strategy and engineering/architecture. (I imagine relative and absolute positioning are an important factor for a race that hunts by flying.)