Elric is dark apocalyptic fantasy, with dragons/demons/magic. There's a dying empire of cruel superhumans, with a values/morals system that is totally alien to humanity. Humans themselves seem to be in a fairly squalid state. The books are set at the end of the world (well
that particular end of the world - it's a Moorcock thing
).
Hawkmoon is post-apocalyptic. Humanity is thrown back to a (late-ish) medieval level, with "science" as the remnants of a slightly post 20th century technology, badly misunderstood from fragmentary remains (there are also some more
extremely advanced technologies, just to spice things up a bit more). Moorcock apparently got some enjoyment out of making the "evil empire" an evolution of Great Britain, and having a German as the good guy.
These were written in the 60s post-war/cold war era, a time when they actually functioned as a fairly literate social commentary on the way politics was evolving. If you want to really intellectual/scholarly/analytical about them, they could form the basis of a decent college paper.
Both settings deal with the conflict between Law and Chaos - not in the D&D sense, although the terminology is the same. It's totally explicit in the Elric setting, and totally "behind the scenes" in the Hawkmoon setting. Moorcockian Law is stability and control, but ultimately sterile, bland and uniform - think the "heat death of the universe" as a more extreme example of how far it will go if left unchecked. Moorcockian Chaos is vibrant, fertile and creative, but out of control and inimical to life. Think jungle undergrowth as a good analogy.
Both of these are active forces in the multiverse, rather than just personality or character traits. It's been hinted that Elric's gods of Chaos may actually be the inhabitants of the End of Time (from another one of Moorcocks settings), where things get really weird and interesting.
The Eternal Champion him/her self is an agent of the Balance, the force that attempts to keep things in check and prevent each side from going to the extreme. When either side gets too far on top, the EC steps in. In most stories, it's the EC vs Chaos, but there's nothing explicitly saying that the EC cannot fight Law in a universe that's become too strictured.
If Mongoose do the "Warlord of the Air" stories, you'll see a more traditional steampunk setting. More traditional fantasy is present in the "Corum" series; the "Dancers at the End of Time" is weird and funny, and (IMHO) his best, but probably more suited to a one-off than a full fledged game setting. "Von Bek" has a healthy dose of Satanism thrown in (with the usual Moorcock twist on things). All are recommended reading.
