It is hard to compare the two because it is two different fantasy worlds with two different types of magic. Dumbledore has almost an endless amount of spells he can cast INSTANTLY and Gandalf seems to wield more elemental power in which seems to take more control and he might not be able to keep up with the pace in which Dumbledore fights with him. Gandalf may come back but the magic in Harry Potter seems more powerful than the magic gandalf uses but I don't know much of the wizards power in middle earth due to the fact that there isn't a whole lot of it in the lord of the rings.
There's no real evidence that truly Arcane magic exists in the LOTR setting, all magic has been Enchantment based or Nature based. I can't really recall any examples of Evocation, Thaumaturgy, Divination, or Transfiguration.
All I can remember are lightning/fire/illumination/ Force ? (like when him and sarumon duke it out) based spells from gandalf, these are from the movies though and I only read the hobbit/the 2nd LOTR book. Don't remember him using much of anything in either book.