One of the strengths of FATE is that it's always been good at being hacked in all kinds of various ways. While I don't know my Tolkien all that well, DFRPG really strikes me as a system that is in a lot of ways a good fit for Middle Earth, with a bit of tweaking.
For example:
-The system would do a great job of handling the power imbalances between elves and other races. They have a set of strong powers (especially the Noldor etc.) but have lower refresh to compensate. You'd probably have to add inhuman/supernatural/mythic beauty as a power, and they'd be pretty much ready to play.
-Mortal stunts costing refresh does a good job of letting someone like Sam (more refresh than anyone) and someone like Boromir (lots of stunts) being in the same party without Sam feeling useless.
-Hobbits should probably have a stunt that gives them positive refresh in exchange for a set of (mostly) penalties and bonuses as the way they're described they seem to have higher refresh than humans (they lack a lot of the passions of men but are very determined when their backs are up against a wall).
-The way items of power work (lowering your refresh) seems to fit the dynamics of the One Right (etc.) beautifully. It is much more dangerous in the hands of powerful (low refresh) people than in the hands of the innocent (high refresh people) since it knocks your refresh rate way down and hits you with nasty compels. I don't think I've ever seen a game that can really capture why it's a much better idea for Frodo to have the ring than for Aragon right out of the box as well as DFRPG does.
-The DFRPG magic system seems flexible enough to handle Middle Earth's magic better than most systems I've seen (certainly better for the purpose than MERP's magic system right out of the box without any tweaking at all).
-A whole lot of the monsters in the game have Catches for their toughness powers already built in.
-Taking a Sponsored Magic power seems to have knocked Saruman's refresh into the negatives.
I don't know my Tolkien well enough to ever run this, but it'd be damn fun to play. It really seems like an almost perfect fit.