Militarily: Westoros is more advanced I guess. But I don't think any part of human history was dominated by the odd type of warfare we see in Essos, so I don't know how to judge. Overall Westoros is a far more militant culture than what we see in Essos barring the Dothraki.
Socially: We don't really know enough about the social structure of the Free Cities outside Bravos and Volantis to judge. Slavery and serfdom lived side by side in our world for a long time. Essos practices more "classical' slavery than the more modern "chattel" slavery. The cartoonish amounts of slaves in some of Essos probably gives this to the Westorosi as well, however I would say Bravos is the most advanced social society we've seen.
Technologically+Medically: Essosi seems to produce more luxury goods(Myrish laces, lenses). We don't see much in the way of Essosi medical care(nor much detail on Westorosi for that matter) so that's hard to judge. Probably would lean to Essos here.
Economically: Essos appears to have a far more complex economy than Westoros does. Part of that is due to being mad up of different nations but still, got to give this one to Essos.
Edited by Ser Marlo the Black, 26 March 2014 - 03:39 PM.