Yes indeed, in simple terms we would be yelling louder than the neighbour.
Pick a non overlapping channel to minimize any disruption (1, 6 or 11 only), also check no one else is using the overlapping channels while making your choice. My understanding is if everyone sticks to 1, 6 or 11 then the devices cooperate with each other rather than simply shouting louder and drowning each other out.
If your wireless is OK then there is no reason to play with power levels and such.