Books:
Harry Potter- Rowling creates a world parallel to our own, filled with generic magic and with child characters. A nice fun read, but I think they went downhill after Book 4, though it might just be me getting older, and anyway, I enjoyed Animorphs more at the time. As I've got older, I've realised that this might be because she can't convincingly pull off the emotions of the characters after this age, and even Book 4 was a bit of a stretch at the end. On the other hand, I can see her difficulty, as writing the realistic thoughts of a teenager might be a bit much for the child audience. Still, great fun to read, but by no means legendary.
The Lord of the Rings- The world Tolkien creates is so rich and realistic, so deep and complex that it is amazing. Another thing I loved about it is that while everyone has their own backstory and agenda, they are neither ignored nor become the focus. The characters just carry them the entire time, but they are not forgotten as soon as the quest begins, or overly fleshed out- just the right amount to remain interesting. The focus is always the War of the Ring, and while other things happen, this focus never disappears, except for the ending once it is over. The same thing goes for the storytelling. While obviously having a Catholic bias, Tolkien never once sacrifices the story because of it. The story came first, and then seeing whether it fits in with his values came second (though apparently he did struggle with this in the Silmarillion, but that's a separate issue). I'm not even going to being to mention the detail he put in to make sure that the names of places were just as distantly related to English as he wanted, or how he constructed different dialects and languages within his created languages and how they varied over time, but it is amazing. He taps into mythology and creates a world that makes sense on its own.
Films:
Harry Potter- The films were the opposite of the books- they got better as the series went on. Again, fun to watch- it had a good mix of being emotional, suspenseful and funny, but it wasn't life-changing. Obviously, special effects were good, but a lot of character development was missed out.
LOTR- Amazing. It might be because I saw them before reading the books (not the Hobbit though), but I really still do enjoy them. After reading the books, I was initially disappointed that they hadn't put in Tom Bombadil and the Barrow-Downs, but now I realise that while the latter could have been amazing and possibly terrifying (though not likely, as the Army of the Dead parts could've been so much scarier), the former would've totally changed the mood. I do think, however, that a few things were ridiculous- Elves at Helm's Deep, Faramir taking Frodo to Osgiliath and the Nazgul being within touching distance of him, Gandalf vs Witch King (extended edition), and a few other things.
They are still in my top ten films of all time, however.
So, my verdict.
The Lord of the Rings wins on both counts.
And let's not even begin to talk about how much Rowling borrowed from Tolkien... Aragog and the other spiders in the Forbidden Forest vs the spiders in Mirkwood, The Whomping Willow vs Old Man Willow (in the LOTR books)... the list goes on...