I'm afraid I beg to differ with much of what's been said here. On this one, I have to say that I think Tolkien's prose is one of the strong points of his writing. Like Lovecraft, Eddison, Dunsany, Machen, and several of the writers who had a distinctive style -- and who, note, have been frequently, usually disastrously, copied -- they ignored the conventions and went their own way. The old-fashioned approach Tolkien used is precisely why these books hold together. They are carefully crafted personal visions, intended to convey something deep within the author himself. The fact that a modern editor wouldn't stand for the slow approach -- or the abandoning of Frodo and Sam for several hundred pages to concentrate on other parts of the story -- simply says that they're too limited in their approach. This was a commonplace in much of 18th and 19th century literature, and people certainly had no problem with it for two hundred years. The problem, I feel, is that we've all grown up in a world with motion pictures, television, and disposable reading matter that often goes for the lowest common denominator, where the intent is to sell books, not to say anything meaningful or to share one's insights or to put on paper something which moves you deeply in a way that will also touch others. That's what these writers did, and that's why, whatever their faults, THEY WORK! To try to tell the stories in any other way would mangle the very vision they were trying to convey. Each of these writers worked, reworked, and re-reworked looking for the precise term that would convey the subtlest nuances of feeling and association they were trying to pin down. Whether one likes their style or not is very much a personal choice; but I'd challenge anyone to try writing these stories in a different way, and see just how badly such an attempt fares -- no matter how talented the writer. The message and the medium (or style) are very much the same here; and I'd say we're all the richer for the fact they DIDN'T follow what was expected of them. Look at the huge number of writers who began well, showed great talent and incredible vision, and then tried to please editors and readers more than to say what was in them waiting to be said, in their own way. With very few exceptions, they're completely forgotten today, because they lost that inner light, and began to simply sound generic. (This happened with the Gothic writers, as well.)
Incidentally, I believe Tolkien's complaint was that Lewis' stories were simply too explicitly allegorical, a type of writing he frankly despised. He felt it was like hitting the reader over the head with a large mallet, rather than giving them freedom to ponder.