I think it mainly depends on aircraft type.
The Europa monowheel really wants to be landed using the crab method - it's single main wheel is in the centre of the aircraft, and if you land wing-down, you'll land with the outrigger first - risk of damaging the outrigger, or groundlooping, or both.
Airliners always seem to use the crab method, too - I've heard various reasons for this, including being more comfortable for pax, and not enough clearance below under-wing engines to approach wing-low. Never heard of a definite case of fuel-starvation due to approaching wing-low, although it's certainly believable. In fact, the
engine failure on G-WLAC a couple of years ago is believed to be due to fuel starvation of this kind, although it was never proved and couldn't be repeated - and that's a high-winged aircraft!
On the other hand, with many very light single-seater or two-seater taildraggers, you'll find the accuracy needed to de-crab at the exact time needed to avoid any drift is very hard to achieve, and you're much better off with the wing-down method - de-crab a fraction of a second too early or too late, and you'll risk ground-looping.
However, I think most training aircraft would be perfectly happy with either method, or with the combined method. Therefore, get your instructor to demonstrate all three, practice all three, and decide what you like best.
Personally, I was taught the crab method, but never really got the hang of it. On my skills test, I completely screwed up a cross-wind landing. The examiner passed me, but suggested I not only get some cross-wnid practice with an instructor, but also ask the instructor to teach me the wing-down method. I did, and I found the wing-down method much easier. (I've now got to learn the crab method, though, because I've bought a share in a Europa monowheel!)
Practice, practice, practice!
FFF
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