I have not attacked the Aztecs in my campaign, I made peace with them lol. I did take over Brazil and Cuba and North American. Since these were settlements I never really fought a open field battle in the new world, though

I suggest using a stern hand with the new world, at least in my experience its better to build cities than castles. The populace is prone to rebel alot even if you converted the lot of them. Imagine upgrading your city/castle with huge walls and towers only to then be kicked out by the populace with a full stack. The same walls you built are the same ones you'll have to attack. I've even seen the native population use horses from one of the stables I built! Don't give them guns!! lol