Critical essay: Paul Edmund Thomas, "Some of Tolkien's Narrators," in Tolkien's Legendarium: Essays on The History of Middle-earth, edited by Verlyn Flieger and Carl F. Hostetter.
The thesis of Thomas's essay is simple: the opening of The Hobbit is told by a very intrusive narrator [*], but as the book gets more serious toward the end, the narrator recedes; and by the start of The Lord of the Rings, the narrator has become impartial and self-effacing, presenting many more viewpoints than at the start of The Hobbit.
Thomas develops this by discussing The Hobbit's narrative voice at length, showing how it fits with the nature of the opening as a children's story. He discusses the initial drafts of LotR, which were unsuccessful attempts to return to the intrusive voice of the start of The Hobbit. He then back-tracks to say that this shouldn't actually be a surprise because of the change of voice at the end of The Hobbit as things got more serious, and the evolving seriousness of LotR itself.
This essay makes a good point, but since I'd pretty much forgotten the voice of The Hobbit, it didn't answer a question I had. Also, I think it probably could've been made just looking at the published texts, without resorting to the drafts. I will be on the lookout for any times when the narrator actually intrudes now, though.
[*] Thomas recounts a system from Wayne Booth's The Rhetoric of Fiction that characterizes narrators on a scale between unintrusive and intrusive, based on three factors: their revelation of information, their interpretation of the stories they tell, and their self-consciousness of their roles as tale-tellers. This is probably familiar to a lot of people already, but I found it useful in a "hey, labels for stuff I instinctively recognized!" way.
Thanks to calimac for recommending this essay.