After completing New Spain's campaign, I turned "to the other side", so I played Apache's one.

Economy.
First I noticed that provinces are really short on population, consequently even cheap buildings quickly used all the money from the treasury. Moreover unit support is cheap, but not the unit production! Taking the fact, that each battle costs you lives and units, the money is a bit issue at the beginning. War paths help a lot, however you can't make them very often. What really brings you money is taking your south neighbour's settlements. Taking a >10k population city brings you a lot of gold from Raid and from further farming. Good I never experienced high riot level.

At the beginning you are really short on infantry units. You can hire ones during warpaths, but they will eat all your money for the support after warpath is over.

Facing European factions
All negative experiences I earned playing for New Spain has proved themselves here:
1. Musketeers are of a little use - they have long recharge speed and are slow. After all they are easily bitten with your apachean scouts which can hide aside and then run for them after main forces are in battle.

2. Bombards can't hit the target from the long distance - it misses most of the time. Canon units are easily bitten with the same scout ones.

3. Cavalry need to get involved in a melee, where they are not that strong as when they are charging. Then get them killed with surrounding archers and braves. The best is to get cavalry charge in a rough terrain (hills, trees, buildings), so charge effect is minimized.

4. Crossbows need to be attacked by melee units, - they loose hand to hand combats.

5. The most challenge remains for the heavy armored infantry. Envelope them with your infantry having medicine men chanting behind and braves throwing morale killer spears. In my case they simply route after I got won with all other units and applied described technique.