For me, LotR was way more fun than Harry Potter. About the only part of the books I really enjoyed other than scenes/moments here and there were when Snape or Lupin was onscreen. They were the only characters who seemed to me to have any depth to them, and I just can't enjoy fluff for fluff's sake. Maybe that's a failing on my part. So when I count "funness," LotR comes out above HP every time. As I said, the only objective point that I think you can give to HP is accessibility, and that I certainly will grant. I just don't find accessibility to be particularly endearing or worthwhile in itself, and HP's characterization, plotlines, themes, and general use of language were all inferior to LotR, in my opinion. Hell, even in YA fiction, I find D.M. Cornish's "Monster Blood Tattoo" series or Terry Pratchett's "Bromeliad" trilogy to be much more enjoyable and higher quality literature than HP.
Don't get me wrong; I don't hate Harry Potter. (Okay, I hate HIM, the character, but not the books that bear his name.) I just don't find them to be, in absolute terms, particularly good books. They are noteworthy for their popularity, which I suspect is due in part to their accessibility, in part to their harmlessness and high levels of light-heartedness, and in part to sheer luck. I'm not mad that they exist, and I don't resent J.K. Rowling for catching hold of that lightning bolt. They've given me mild enjoyment for several hours of my life. But I likely won't be buying them for my children (if they ever exist.)