Living in Southern Africa, I have seen and heard lions roar.
The MGM one seems completely plausible to me.
They are big cats. They need to display authority, or at least identify as a “top cat”. Lions live in packs, so there is some need to say “this is my pack, fuck off”
Tigers, to the best of my knowledge, do not roar.
They live very solitary lives until mating time, which is a extremely quick (pity the lady tigers!)