Ah, the cmplex subject of engine braking!!
In days of old, when ............... and brakes were of the 'drum' variety and you were fortunate if you had twin leading shoe rather than the single leading variety the eficiency of the brakes was, to put it mildly, complete pants. Therefore it was always prudent to use engine braking to assist the pitiful wheel braking system.
With modern disc brakes this is, generally, no longer necessary and in general driving then it produces less strain on (expensive) engine components more on (less expensive) brake components i.e. in normal day-to-day driving don't do it.
If, however, you want to embark on some, shall we say, spirited driving then there is always the risk that the brakes will overheat and fade will set in. In this scenario it is better to use engine braking as the brakes should remain efficient for longer.
Now we turn to rear wheel drive v front wheel drive v four wheel drive. Engine braking will only apply 'braking effort' to the driven wheels. For the F/TF this is the rears only. In dry conditions not really a problem but when it is wet/greasy the braking effect on the rear wheels in conjuction with the lightening of weight on them as the vehicle mass is transferred forward can cause the rears to lose grip completely and result in a bit of a 'shimmy'. If you are not in a straight line at the time and are negotiating a corner then this can get very exciting. Use engine braking on rear wheel drive cars very cautiously in wet conditions otherwise you may induce a bit too much oversteer (great for rallying by the way).
The same logic applies to front wheel drive cars except that you can induce more understeer, so be wary.
Four wheel drive depends on whether it is full time or not. Generally it is a lot 'safer' to engine brake in four wheel drive cars in slippery conditions. However, there are a few e.g. Audi TT that are not full time four wheel drive and act mainly like a front wheel drive car when engine braking is applied AND the brakes are being used simultaneously (under braking the Haldex unit does not transfer any drive to the rear wheels)
So. it's 'horses for courses' - just be careful!