In response to something written on the Nausicaa Mailing List:
I'm not a big fan of "Princess Mononoke," but Tolkien's so-called complexity is mainly surface dressing: a lot of made-up history, some invented languages, so on and so forth. On an emotional level though, he's pretty much straightforward--the good guys are good, the bad guys bad (painfully bad--only Saruman is sketched with any detail, while Sauron is a big ball of gas), save for Gollum, his one successfully complex character. More like the exception that proves the rule.
Miyazaki's features may not have the sweep of Tolkien (except for his "Nausicaa" manga), but I think he achieves a level of emotional complexity in both films and manga that goes beyond Tolkien. The question is not even worth considering seriously.