Purring vs. Roaring Cats
Citation below from a free PMC article (open access, full text, PDF download available).
Summary: Smaller cat species can purr because they can twitch their vocal cords rapidly. Big cats can't, because their vocal cords have thick tissue pads on them. Contrary to earlier hypotheses, whether or not the hyoid is bone or cartilage has nothing to do with it, it merely allows the larynx to be lowered to give them access to lower vocal ranges (which arguably helps with more impressive roars, along with those aforementioned tissue pads).
The distinction between 'roaring' and 'purring' can also be tentatively clarified in terms of the function of the vocal anatomy. Purring is caused by extremely rapid twitching of the vocalis muscle (running within the vocal folds) (Hirose et al. 1969; Remmers & Gautier, 1972; Frazer Sissom et al. 1991). A large flexible pad like that seen in the vocal folds of the Pantherinae would tend to damp such twitchings and thus make it difficult, if not impossible, to purr. However, the elastic epihyoid of the Pantherinae has an independent function: allowing the lowering of the larynx, with concomitant lowering of formant frequencies. This adaptation is in principle quite independent of any change in the larynx, and thus has no direct effect on the ability to purr.
– Weissengruber GE, Forstenpointner G, Peters G, Kübber-Heiss A, Fitch WT. Hyoid apparatus and pharynx in the lion (Panthera leo), jaguar (Panthera onca), tiger (Panthera tigris), cheetah (Acinonyxjubatus) and domestic cat (Felis silvestris f. catus). J Anat. 2002 Sep;201(3):195-209. doi: 10.1046/j.1469-7580.2002.00088.x. PMID: 12363272; PMCID: PMC1570911.