My biggest problems with Assyria have been that whenever I roll them I seem to start off miles of rough terrain away from my nearest neighbor, which makes conquering with the siege towers a pain, as they are really really vulnerable before promoting them with cover and take a while to build. Also, as much as you're pumping hammers into unit production, you need to remember to get your Royal Libraries built in every settled/conquered city, at least those on your battle frontiers, and to get your Writer's Guild and National Epic up quick, so that you can get the extra XP for new units. Remember that you can move your great works of writing around as need be when building your military!