I am not sure I can remember all the major difference in C3, but one of the biggest is the way leaders and armies work. Leaders in C3 can rush anything, so it is often best to use them for structures (wonders), rather than an army.
In C3C, you have two types of leaders. SGL can only rush improvements, while MGL rush non wonders (in the main). This means you will mostly use an MGL to make an army.
Armies are your best means of playing AW. In C3C armies get several boost. One is to add an extra movement. Another is allow free pillaging, no use of a movement point. Armies are able to heal in all lands, without a Battlefield.
An important considerations in AW is too nearly always be making troops and settlers in all towns.
I think the biggest is to stick to CxxC placement as much as you can.
Do not go out exploring as you do not want to met others and have to DOW. The more nations you know and are fighting the harder it will make it. There does come a point, where it does not matter as the new ones are so far away.
Build as few structures as you can in all, but the best places. Get barracks up in all the places making troops. Those without one should make cats or whatever bombardment tech you have.