Judging from the manual
- A loss of effectiveness reduces a vehicle's movement speed (manual p.15). It is calibrated in a way that at 50% effectiveness, a vehicle moves only at 75% of its max. speed.
- Fire Combat: The effectiveness of a vehicle affects its firepower (it modifies the fire value, p. 36). There is no effect on its defensive power in fire combat - the resilience of a vehicle is only determined by its armor value and by whether the vehicle is immobilized or not.
- Assault (p. 56): When it comes to determining a vehicle's offensive assault power, a vehicle's weapons and - unless immobilized - its armor value matter. If the vehicle's effectiveness should also taken into account, then the manual forgot to mention it. The defensive power of a vehicle in assaults depends entirely on its armor value and on whether it is immobilized or not.
So, to sum it up, it seems as if effectiveness only affects the movement speed and the fire power of vehicles. But it neither affects the defensive parameters of a vehicle, nor its performance in assaults.