>Are there any definitive anthropomorphic worlds/stories on the same scale as Lord of the Rings or Star Wars in terms of depth?
Not really. The Western anthropomorphic tradition arose in the context of allegory. Note that the man behind the former work you wrote, despised allegory in all its forms. Star Wars also bares little allegorical. They're both fictionalized histories set in the far distant past, like the Hyborian Age.
Anthropomorphism of animals came about by the Christian clergy who wanted to parallel antediluvian beasties like the Leviathan or half-human half-beast demons like Lilith. They used such figures to decorate the margins of their scriptural writings. It served both as critique and reinforcement/propaganda toward the current social order. People thus began to take these animals and apply them to their own allegories by the Early Modern period. By the Industrial epoch, a rich tradition in anthropomorphs had developed in England who used such animals to parody and draw allusion to their current rapidly-changing lifestyles. Cats were a common, popular theme, as the works of Louis Wain demonstrate.
This folk tradition became the first cartoon or funny animals, and the rest, as we say, is history. Few writers, however, breached beyond children's stories to create a living mythos. The entire idea of going back into the past and rewriting folk tales into fictional histories, started with Tolkien. Because of that, it postdates the sixties. There were only about two decades between then and the first furry con. So there was never much time for a prospective writer to generate such a history before, well, they were overruled by the degenerate squad. Maybe we'll see some in the future, since the modern furry generation seems very interested in high fantasy. Children's stories have always been the mainstay of anthro art and writing, so that's what most creative attention is devoted to. Porn makes up the remainder. And there's only so much depth you can stuff in either.