For me, the best way to deal with natives is to be defensive yet flexible. I'm about mid-game (in the RTI).

My army usually consists of:
1-2 artillery (always have at least one howitzer)
General
4-5 Line infantry
2 Dragoons
1-2 light dragoons
2 Regiment cavalry
and occasionally grenadiers or rangers

With this army (usually around 1200 strong), I can take on a native army about 1600 without much trouble.

My plan is to have the line infantry in rows of three spanning in front of the artillery (they have fire-by-rank). Rangers/grenadiers on the flanks just in case I can't catch a flanking unit in time with my line infantry. Dragoons and regiment cavalry are always hidden somewhere on the flanks, as I bring them in only when A) I really need them, or B) there is a weak spot in their army. No need for unneccessary casualties. Finally, my General sits behind the artillery.

I let them get beaten down a bit by the artillery, until either they charge me or I have to move in on them. If they charge you, make sure everyone is on fire at will and defensive positions, and the line infantry will slaughter them. Be prepared to have your units on the flanks curl back on the sides just in case a unit tries to get around you. If you need to move in, leave units with your artillery and move the rest of your army en masse. When the timing is right, you'll have them backed into a corner, this is when you have your men double time it and quickly form a U shape around the enemy. If done right, you'll slughter them.

But above all, be ready to send in cavalry to help, and be ready to move your flanking troops into either defensive or offensive positions when need be.