Both landings are done when an airplane's nose is not in inline with the runway. How are these two different? when should one technique be preferred over other?
Consider where the center of gravity is in relation to the main wheels. If you are in a tail dragger, you definitely would prefer to de-crab (never heard that term before now) before touching down. If you touched down while crabbed, you'd have a moment created by the center of gravity around the main gear to ground loop the airplane.
In a tricycle gear airplane, that same moment would work to straighten the airplane since the center of gravity is forward of the main gear.
In a crosswind from the right, for example, when you apply left rudder to align the aircraft with the runway, the right wing will want to come up (you just gave it a little extra speed), so you will want to use right aileron to at least counter that as you certainly don't want the crosswind component to get 'under' the wing.
Both 747 operators I flew for recommended touching down in the crab. Personally I didn't like that and used a combination approach in a heavy crosswind, take out some of the crab but not all. Also, while they did caution against lowering the upwind wing, I always lowered the wing a little. I once figured out how much the wing would have to be lowered before ground contact, and it was quite substantial, more than I would ever think of using. Also, as I remember, It would not be the wingtip or an outboard engine pod that would make first contact, but rather the outboard corner of the outboard wing flap when set to flaps 30.
Finally, when your touch down speed is 140 knots, for example, you'll have to crab much less for a given crosswind component than if your touchdown speed is 70 knots. Cosine or tangent of the angle, I forget which.
Wikipedia's definitions are a bit unclear but it seems to say that de-crabbing is where you straighten the aircraft in the air just before touchdown; crabbing is where you straighten on the runway after touchdown.
Just before the flare, opposite rudder (downwind rudder) is applied to eliminate the crab
upon touchdown the airplane tracks towards the upwind edge of the runway while de-crabbing to align with the runway. Immediate upwind aileron is needed to ensure the wings remain level while rudder is needed to track center line. The greater the amount of crab at touchdown, the larger the lateral deviation from the point of touchdown.
Personally I find these definitions odd: in my limited experience in light aircraft, a "crabbing" approach is what Wikipedia calls "de-crabbing", and "de-crabbing" is the action of straightening the aircraft in the air before touchdown. I have no idea why a pilot would prefer to land the aircraft at an angle to the runway and then correct on the ground. But perhaps this is normal practice in larger aircraft; I have no idea about that.
It also depends if you have a low or high wing airplane. And if you are comfortable touching down on one wheel.
In my plane, A Socata TB, the plane has a monstrous rudder that has a demonstrated crosswind component of 25 knots. That's demonstrated, I'll tell you it has the authority to do more but the manufacturer always errs on the side of safety. It also is a low wing, so high crosswind landings get be nervous that I might scrape a wing edge.
To me being sideways is not normal. Crabbing to the runway means that you are heading at the runway but it may not be at your nose. But it is holding a steady view relative to a point on your windscreen. Remember, the training if you see another plane. If it's moving relative to a point on your windshield that's good. If it's not and maintaining the same point, you are generally on a collision course. Same with the runway numbers, if they are off to your left and the runway is coming at you, you might be pointing at the control tower but your "Ground Path" is straight down the runway.
I'll crab all the way down, then bleed off energy using the T-6 P-51 training I received, then just as I feel the final drop beginning, I'll add about 2 inches of MP to arrest the decent and kick out to point the nose down the runway.
Remember, the only time your wheels have to be straight down the runway is 1 millisecond before the rubber hits the road!
Also in retrospect, I assume the turn Crabbing is derived from the way a real Crab moves. It walks sideways to go forward.
It all depends on the aircraft you are flying. Some jetliners are certified to be landed with side loadings if that side loading on landing is within certain limits. Some airliners like the 737 require the jet to be landed in a crab as cross controlling to keep the nose aligned with the runway centerline runs the risk of scraping and damaging one of the engine nacelles on the runway.
Light GA aircraft are not designed to take high side loads on their landing gear and require cross control to align the jet with runway centerline during crosswind landings. In an airplane fitted with conventional landing gear (tailwheel), it is imperative to land parallel to centerline with good crosswind technique as side loading creates a strong possibility on inciting a ground loop.