Both methods work equally well. The reason for the difference reflects the different objectives between the bulk of FAA training and the bulk of CAA training.
NOTE: This is not intended to suggest either type of training is better than the other, that is a separate argument!!
In the main, FAA training is geared towards putting the trainee into a light aircraft and the techniques are taught accordingly. However, much UK training is geared towards a professional licence and flying the big jets. In the latter case, if you use the wing-down technique, you stand a good chance of leaving some or all of the engine pods at the touchdown point.
Horses for courses.