Barbarians spawning more aggressively in the early game, but only if you can't kill the scout before they get back to the camp.
"Eurekas" which decrease the time it takes to research certain technologies and civics. For example, if you kill a barbarian with a slinger (the unit that predates the archer), you can research archery in half as many turns.
The civics system is quite cool as well where you select policy cards that will give you different bonuses. The type of government that you choose affects the type and amount of policy cards that you can select.
The big change versus CIV V is the districts system. Not every city can be good at everything, and you'll find that your cities will be more specialized (science output, faith output, commerce, military, navy, etc.). Also, because of the way that bonuses for districts work, I find that you really have to adapt your city planning to the map.
Also, wide play styles are generally better in CIV VI whereas in CIV V tall play styles were far more advantageous.
