RJ, you just need to be as up on LOTR as you are on HP. And that doesn't mean just movies.
So as soon as you're done with The Simarillion [which I have just badly mispelled], The Hobbit, and all three books of The Lord of the Rings, only then can you answer this question with no bias.
Personally, I'm for HP. Most of the LOTR lot will be fighting with swords, arrows, maces, shields... all of which wizard spells top. Wizards can make LOTR's weapons turn on themselves. We don't even know all the spells in the Harry Potter canon, but we know that great wizards can create new spells and that the spell library probably expands hourly.
We can't really compare the wizards in HP to the wizards in LOTR... their magic is very different. But overall it seems that HP wizards are faster with their work, and LOTR are classic, must find portents and relics and dig through piles and piles of old parchment and know fifty million languages...
And preparing for battle takes a long time. During all the preparations, wizards can K/O most of the LOTR crowd. Of course there are exceptions. Ents, the Maiar, Elves, and perhaps some members of the Fellowship.
But HP wizards also try to be efficient and leave innocents alive. In this situation, they would need a very good reason to kill the citizens of Rohan and so forth.