I've never been a big fan of the Realms, partly because of the blatant munchkin power boosts in its splatbooks, partly because every FR innkeeper is a retired 8th level adventurer, and partly because of all the drow fanboyism. That's just me though. Stripped of those negative elements, it seems a decent enough standard-fantasy D&D setting.
Eberron, I am a big fan of. What I love about the setting:
Religion. The religions of Eberron feel real, to me. The gods are distant and unreachable, and as a result there are many, many, different faiths and interpretations of each faith. Much like the development of real human religions. The Greyhawk/FR-style pseudo-greek pantheons that are treated in a very non-pantheistic manner never made much sense to me.
Organizations. The setting is jam packed with all sorts of different power groups motivated by self-interest. Each and every one has clear goals that naturally set them against each other and against the players (or for the players). There's no clearcut right and wrong in some cases, and the PCs could find themselves working alongside some very bad people in order to stop a common enemy. Or opposed by "the good guys" as the players try to correct an obvious (to them) wrong. It's like a goldmine for adventure ideas, and as with the religions, it feels very much like actual human politics.
The intrigue. Related to the above, but the normal starting period in the setting - just after a truce is called in a 100-year war of succession that had no victor - is just filled with all sorts of cloak-and-dagger adventure possibilities.
The pulp elements. Aside from the obvious - fighting on top of train cars, airship pirates, etc. - the setting has a lot in common with the inter-world war period in which the pulp genre developed.