Actually dtna7 is right. Having 4WD only serves to divide the torque and power to more driving wheels. With less power/torque at each wheel they become more manageable and all that power spreads across a greater surface for better traction.
It can't be called traction control because by definition traction control is controlling the amount of power and torque a drive wheel has, by braking or throttle feathering. Going from 2WD to 4WD is nothing like traction control. But, because it does make the car far more tractable it gives a bit like the effect of traction control, but not doing anything that a traction control does.
But, dtna7 can at least be a bit less on the offence (for a lack of a better word).

But hey, no hard feelings between you two, ay?
On a side note, for normal city driving it's better to be in 2WD. The engine will experience less frictional losses and frees it up from having to drive all 4 wheels. Therefore you save more fuel. Doesn't matter if the car is heavy with load, if you have enough traction stick with 2WD. If you're starting on a slope, the 4WD may help because in 2WD the ASX as I understand it is essentially a FWD, but if you already have momentum going to a slope even 2WD is fine (you hardly see any FWD vehicle spin their wheels after a run up to a slope do you?).
In heavy rain or driving on anything that you think will offer you less traction, use 4WD. Simple.
This post has been edited by VagueConcerns: May 21 2014, 05:32 PM