Warhammer's world is richer and more full than Warcraft's, and while LOTR has a huge variety of cultures and elements, it doesn't have the variety and vibrance of Warhammer IMO. Warhammer has their equivalents of Mongols, Scots, Vikings, Medieval Kingdoms, Mayans etc. LOTR is basically just Anglo-Saxon/Celtic mythology with a few bits of Africa and China on the sidelines.

If we're talking crossover battlegrounds, then that depends on the era. If it's Warhammer vs LOTR vs Warcraft, Warhammer wins easily based on the prominence of magic and giant beasties, but all three would be smashed by Silmarillion. A Silmarillion mod would be really awesome, though it would probably take as much work as Warhammer :P