Not going to touch the similarities, as I can't speak from a basis of knowledge, but there is one big difference I can address.
The big difference between Harry Potter and LOTR, is that Harry Potter is palatable.
A few years ago, I sat down with the first lord of the rings movie, a bag of popcorn and rather significant expectations (given all of the hype being pumped around by the ring-suckers)....
75 minutes into the first movie, I was completely and utterly un-engaged. One hour and fucking fifteen minutes into this boring movie, there's zero character development, seemingly zero action/plot movement....
then I thought. "Shit, Randall Graves was right. They were just fucking walking." pitiful!
...now maybe it gets better. who knows. But let me say this. I'm by no means a need-it-now type of person. I am more than willing to let a movie slowly unfold the plot. (Hell, I'm a huge fan of 'Where Eagles Dare' so that should say something). But when a movie like the 1st Lord Of The Rings takes more than 75 minutes for any worthwhile character or plot development....it's not worth wasting any more time. If the rest of the movies are anything like the first 75 minutes of LOTR, it's a waste.
I'm still skeptical...because each and every time I see a clip from one of the LOTR movies, I see them walking...nothing else. (Not to mention that Randall, again, seems to hit the nail on the head with respect to the hobbit's gayness)
Now, take Harry Potter....I was sucked into the first Harry Potter movie within 5 minutes. I hadn't read a lick of the books, but enjoyed the movies so much so that I've seen them all multiple times.
You need a damn good story to make a good movie.......but you can also ruin a damn good story with a shitty movie. It seems to me that the HP applies to the former and LOTR applies to the latter...