I know of no "not-LotRs" trying to copy the look of the films, but you might look at historical lines from either Magister Militum or Kallistra. Kallistra's High Elf cavalry also could easily pass for the Knights of Dol Amroth, or if you want a plate look, try 100YW or War of the Roses Knights, or for a different slightly exotic approach, go older with Byzantine Cataphracts.
As for the Men of the East, take a look at Arabs, Ottomans, Late Persians, Mongols, or among the various cataphract armies if you want a more exotic armored look.
I wish somebody did this guy (as mounted cavalry) in 10mm:
He's a Scythian, but man, what an exotic look! Would make nifty Men of the East, or any fantasy force! (Plus, not too hard to paint. Some red, some gold, a wash for the shadows, and you have an awesome looking force (that would be quite reflective of Tolkien's description in the novel, too.)
Alas, nobody does these in 10mm, as far as I can find.
