The Hobbit is a better-written and more cohesive story, the characters are more likable and more defined. To judge a story by its number and scope of battles is frankly puerile, and it's led to plenty of authors attempting to give a story 'legitimacy' by just tossing in conflict that doesn't really add anything.
Both stories overstay their welcome and end up having fairly unfulfilling endings (or, in the case of Return of the King, several serial unfulfilling endings); the Jackson films of the Hobbit have at least thus far played up some of the more minor aspects of the book, and some of those are really interesting played up, like Dol Guldur and the Necromancer. The Rankin-Bass work similarly did a good, if brief, adaptation keeping in the sense of music and adventure and not harping so much on blah blah warfare.
Lord of the Rings has been built up for decades by fans. I liked the story when I was a child, but as I grew older I realised that what I liked the most was what it stimulated in my imagination, rather than being very good itself. It started off strongly but couldn't keep it up. The Hobbit is, on the other hand, a pretty solid and consistent story with pretty solid and consistent characters. There are fewer in the cast of characters, but they are much less two-dimensional, one-note characters than the majority of the cast of Lord of the Rings.
My vote goes for The Hobbit on this one, even if I'm a little late in weighing in here. As someone who has read the books and seen almost every adaptation of each story, there's simply no comparison when it comes to telling a coherent and enjoyable story.