So Harry Potter definitely has the cooler wand, the massive number of spells, trained deathmatches, etc. But the Wizards from Lord of the Rings are infinitely more powerful (If you delve into the Silmarillion and some of Tolkien’s letter and writings, in essence demi-gods restricted in their power). Personally, I think Gandalf would kick Dumbledore’s @$$. And not just because Dumbledore ‘Shall NOT PASS!’
(And neither would Harry, if Gandalf was his professor)