I like them both a lot too- The original trilogy were, I think, the first live action movies I ever watched. Also a bit ironic since (as movies) we're comparing an action/adventure series to a character drama series. (My two favorite genres)
All in all, Lord of the Rings wins in my book. Peter Jackson is an amazingly expressive filmmaker. George... well, the only things I've seen that he's done on his own that were decent were the Star Wars films because they're the only things that he really took his time with & thought through. And, even then, he based the series on mythic archetype. As deep as he really got with the characters were good, evil, & plot twist.
Lord of the Rings wasn't a very interesting book on it's part, but Jackson is one of the few filmmakers today who is fully capable & willing to use his direction style to enhance the film & help tell the story, something lots of directors these days don't really do (or, at least, not well) This helps really get into the characters' emotions & allows the viewer to really get into things on an emotional level.
So, yeah, Lord of the Rings, if anyone just wants to skip to the end...